Algebric solution for a simple polinome (n+2) but very long/complex coefficients: solve?

How could we find an algebric solution for a simple polinome (n+2) but very long/complex coefficients (cf below)? We tried with the function solve, but the resolution stops with the following message "Exceed 25 000 characters". Any idea to help us? Thanks

sol=solve('(NO2^2)*( -((O2z*(KmN2*VAR + KmAR*VN2 + O2z*VAR + O2z*VN2)*(4*O2z^2*VN1 - 4*O2z^2*VPs + O2z^2*VAR*gam^2 + O2z^2*VN2*gam^2 + 4*KmAR*KmN2*VN1 - 4*KmAR*KmN2*VPs + 4*KmAR*O2z*VN1 + 4*KmN2*O2z*VN1 - 4*KmAR*O2z*VPs - 4*KmN2*O2z*VPs - 4*O2z^2*VAR*ome - 4*O2z^2*VN2*ome + KmN2*O2z*VAR*gam^2 + KmAR*O2z*VN2*gam^2 - 4*KmN2*O2z*VAR*ome - 4*KmAR*O2z*VN2*ome))^(1/2) + O2z^2*VAR*gam + O2z^2*VN2*gam + KmN2*O2z*VAR*gam + KmAR*O2z*VN2*gam)/(2*(O2z^2*VAR + O2z^2*VN2 + KmN2*O2z*VAR + KmAR*O2z*VN2)))^2*(KmDe+(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2))*(VN1-VD2-VN2*(O2z(1)/(KmN2+O2z(1)))-VDn-VAn)+( -((O2z*(KmN2*VAR + KmAR*VN2 + O2z*VAR + O2z*VN2)*(4*O2z^2*VN1 - 4*O2z^2*VPs + O2z^2*VAR*gam^2 + O2z^2*VN2*gam^2 + 4*KmAR*KmN2*VN1 - 4*KmAR*KmN2*VPs + 4*KmAR*O2z*VN1 + 4*KmN2*O2z*VN1 - 4*KmAR*O2z*VPs - 4*KmN2*O2z*VPs - 4*O2z^2*VAR*ome - 4*O2z^2*VN2*ome + KmN2*O2z*VAR*gam^2 + KmAR*O2z*VN2*gam^2 - 4*KmN2*O2z*VAR*ome - 4*KmAR*O2z*VN2*ome))^(1/2) + O2z^2*VAR*gam + O2z^2*VN2*gam + KmN2*O2z*VAR*gam + KmAR*O2z*VN2*gam)/(2*(O2z^2*VAR + O2z^2*VN2 + KmN2*O2z*VAR + KmAR*O2z*VN2)))^2*VDe*(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2)+( -((O2z*(KmN2*VAR + KmAR*VN2 + O2z*VAR + O2z*VN2)*(4*O2z^2*VN1 - 4*O2z^2*VPs + O2z^2*VAR*gam^2 + O2z^2*VN2*gam^2 + 4*KmAR*KmN2*VN1 - 4*KmAR*KmN2*VPs + 4*KmAR*O2z*VN1 + 4*KmN2*O2z*VN1 - 4*KmAR*O2z*VPs - 4*KmN2*O2z*VPs - 4*O2z^2*VAR*ome - 4*O2z^2*VN2*ome + KmN2*O2z*VAR*gam^2 + KmAR*O2z*VN2*gam^2 - 4*KmN2*O2z*VAR*ome - 4*KmAR*O2z*VN2*ome))^(1/2) + O2z^2*VAR*gam + O2z^2*VN2*gam + KmN2*O2z*VAR*gam + KmAR*O2z*VN2*gam)/(2*(O2z^2*VAR + O2z^2*VN2 + KmN2*O2z*VAR + KmAR*O2z*VN2)))*(p-VN2*(O2z(1)/(KmN2+O2z(1)))*f-VD2*f-VDn*f-q)+( -((O2z*(KmN2*VAR + KmAR*VN2 + O2z*VAR + O2z*VN2)*(4*O2z^2*VN1 - 4*O2z^2*VPs + O2z^2*VAR*gam^2 + O2z^2*VN2*gam^2 + 4*KmAR*KmN2*VN1 - 4*KmAR*KmN2*VPs + 4*KmAR*O2z*VN1 + 4*KmN2*O2z*VN1 - 4*KmAR*O2z*VPs - 4*KmN2*O2z*VPs - 4*O2z^2*VAR*ome - 4*O2z^2*VN2*ome + KmN2*O2z*VAR*gam^2 + KmAR*O2z*VN2*gam^2 - 4*KmN2*O2z*VAR*ome - 4*KmAR*O2z*VN2*ome))^(1/2) + O2z^2*VAR*gam + O2z^2*VN2*gam + KmN2*O2z*VAR*gam + KmAR*O2z*VN2*gam)/(2*(O2z^2*VAR + O2z^2*VN2 + KmN2*O2z*VAR + KmAR*O2z*VN2)))*VDe*(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2)*f-(KmDe+(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2))*e*(VN2*(O2z(1)/(KmN2+O2z(1)))+VD2+VDn)+VDe*(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2)*e+(NO2)*( -((O2z*(KmN2*VAR + KmAR*VN2 + O2z*VAR + O2z*VN2)*(4*O2z^2*VN1 - 4*O2z^2*VPs + O2z^2*VAR*gam^2 + O2z^2*VN2*gam^2 + 4*KmAR*KmN2*VN1 - 4*KmAR*KmN2*VPs + 4*KmAR*O2z*VN1 + 4*KmN2*O2z*VN1 - 4*KmAR*O2z*VPs - 4*KmN2*O2z*VPs - 4*O2z^2*VAR*ome - 4*O2z^2*VN2*ome + KmN2*O2z*VAR*gam^2 + KmAR*O2z*VN2*gam^2 - 4*KmN2*O2z*VAR*ome - 4*KmAR*O2z*VN2*ome))^(1/2) + O2z^2*VAR*gam + O2z^2*VN2*gam + KmN2*O2z*VAR*gam + KmAR*O2z*VN2*gam)/(2*(O2z^2*VAR + O2z^2*VN2 + KmN2*O2z*VAR + KmAR*O2z*VN2)))^2*(KmDe+(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2))*(VN1*s+VD2*KmDn-VN2*(O2z(1)/(KmN2+O2z(1)))*s-VDn*KmD2-VAn*s+p*s)+( -((O2z*(KmN2*VAR + KmAR*VN2 + O2z*VAR + O2z*VN2)*(4*O2z^2*VN1 - 4*O2z^2*VPs + O2z^2*VAR*gam^2 + O2z^2*VN2*gam^2 + 4*KmAR*KmN2*VN1 - 4*KmAR*KmN2*VPs + 4*KmAR*O2z*VN1 + 4*KmN2*O2z*VN1 - 4*KmAR*O2z*VPs - 4*KmN2*O2z*VPs - 4*O2z^2*VAR*ome - 4*O2z^2*VN2*ome + KmN2*O2z*VAR*gam^2 + KmAR*O2z*VN2*gam^2 - 4*KmN2*O2z*VAR*ome - 4*KmAR*O2z*VN2*ome))^(1/2) + O2z^2*VAR*gam + O2z^2*VN2*gam + KmN2*O2z*VAR*gam + KmAR*O2z*VN2*gam)/(2*(O2z^2*VAR + O2z^2*VN2 + KmN2*O2z*VAR + KmAR*O2z*VN2)))*(KmDe+(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2))*(p*s-VN2*(O2z(1)/(KmN2+O2z(1)))*f*s-VD2*f*KmDn-VDn*f*KmDe-q*s)+VDe*(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2)*s*(( -((O2z*(KmN2*VAR + KmAR*VN2 + O2z*VAR + O2z*VN2)*(4*O2z^2*VN1 - 4*O2z^2*VPs + O2z^2*VAR*gam^2 + O2z^2*VN2*gam^2 + 4*KmAR*KmN2*VN1 - 4*KmAR*KmN2*VPs + 4*KmAR*O2z*VN1 + 4*KmN2*O2z*VN1 - 4*KmAR*O2z*VPs - 4*KmN2*O2z*VPs - 4*O2z^2*VAR*ome - 4*O2z^2*VN2*ome + KmN2*O2z*VAR*gam^2 + KmAR*O2z*VN2*gam^2 - 4*KmN2*O2z*VAR*ome - 4*KmAR*O2z*VN2*ome))^(1/2) + O2z^2*VAR*gam + O2z^2*VN2*gam + KmN2*O2z*VAR*gam + KmAR*O2z*VN2*gam)/(2*(O2z^2*VAR + O2z^2*VN2 + KmN2*O2z*VAR + KmAR*O2z*VN2)))*f+e)+( -((O2z*(KmN2*VAR + KmAR*VN2 + O2z*VAR + O2z*VN2)*(4*O2z^2*VN1 - 4*O2z^2*VPs + O2z^2*VAR*gam^2 + O2z^2*VN2*gam^2 + 4*KmAR*KmN2*VN1 - 4*KmAR*KmN2*VPs + 4*KmAR*O2z*VN1 + 4*KmN2*O2z*VN1 - 4*KmAR*O2z*VPs - 4*KmN2*O2z*VPs - 4*O2z^2*VAR*ome - 4*O2z^2*VN2*ome + KmN2*O2z*VAR*gam^2 + KmAR*O2z*VN2*gam^2 - 4*KmN2*O2z*VAR*ome - 4*KmAR*O2z*VN2*ome))^(1/2) + O2z^2*VAR*gam + O2z^2*VN2*gam + KmN2*O2z*VAR*gam + KmAR*O2z*VN2*gam)/(2*(O2z^2*VAR + O2z^2*VN2 + KmN2*O2z*VAR + KmAR*O2z*VN2)))^2*(KmDe+(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2))*t*(VN1-VN2*(O2z(1)/(KmN2+O2z(1)))-VAn)+( -((O2z*(KmN2*VAR + KmAR*VN2 + O2z*VAR + O2z*VN2)*(4*O2z^2*VN1 - 4*O2z^2*VPs + O2z^2*VAR*gam^2 + O2z^2*VN2*gam^2 + 4*KmAR*KmN2*VN1 - 4*KmAR*KmN2*VPs + 4*KmAR*O2z*VN1 + 4*KmN2*O2z*VN1 - 4*KmAR*O2z*VPs - 4*KmN2*O2z*VPs - 4*O2z^2*VAR*ome - 4*O2z^2*VN2*ome + KmN2*O2z*VAR*gam^2 + KmAR*O2z*VN2*gam^2 - 4*KmN2*O2z*VAR*ome - 4*KmAR*O2z*VN2*ome))^(1/2) + O2z^2*VAR*gam + O2z^2*VN2*gam + KmN2*O2z*VAR*gam + KmAR*O2z*VN2*gam)/(2*(O2z^2*VAR + O2z^2*VN2 + KmN2*O2z*VAR + KmAR*O2z*VN2)))^2*VDe*(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2)*t+( -((O2z*(KmN2*VAR + KmAR*VN2 + O2z*VAR + O2z*VN2)*(4*O2z^2*VN1 - 4*O2z^2*VPs + O2z^2*VAR*gam^2 + O2z^2*VN2*gam^2 + 4*KmAR*KmN2*VN1 - 4*KmAR*KmN2*VPs + 4*KmAR*O2z*VN1 + 4*KmN2*O2z*VN1 - 4*KmAR*O2z*VPs - 4*KmN2*O2z*VPs - 4*O2z^2*VAR*ome - 4*O2z^2*VN2*ome + KmN2*O2z*VAR*gam^2 + KmAR*O2z*VN2*gam^2 - 4*KmN2*O2z*VAR*ome - 4*KmAR*O2z*VN2*ome))^(1/2) + O2z^2*VAR*gam + O2z^2*VN2*gam + KmN2*O2z*VAR*gam + KmAR*O2z*VN2*gam)/(2*(O2z^2*VAR + O2z^2*VN2 + KmN2*O2z*VAR + KmAR*O2z*VN2)))*(KmDe+(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2))*t*(p-VN2*(O2z(1)/(KmN2+O2z(1)))*f-q)+VDe*(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2)*t*(( -((O2z*(KmN2*VAR + KmAR*VN2 + O2z*VAR + O2z*VN2)*(4*O2z^2*VN1 - 4*O2z^2*VPs + O2z^2*VAR*gam^2 + O2z^2*VN2*gam^2 + 4*KmAR*KmN2*VN1 - 4*KmAR*KmN2*VPs + 4*KmAR*O2z*VN1 + 4*KmN2*O2z*VN1 - 4*KmAR*O2z*VPs - 4*KmN2*O2z*VPs - 4*O2z^2*VAR*ome - 4*O2z^2*VN2*ome + KmN2*O2z*VAR*gam^2 + KmAR*O2z*VN2*gam^2 - 4*KmN2*O2z*VAR*ome - 4*KmAR*O2z*VN2*ome))^(1/2) + O2z^2*VAR*gam + O2z^2*VN2*gam + KmN2*O2z*VAR*gam + KmAR*O2z*VN2*gam)/(2*(O2z^2*VAR + O2z^2*VN2 + KmN2*O2z*VAR + KmAR*O2z*VN2)))*f+e)-VN2*(O2z(1)/(KmN2+O2z(1)))*(KmDe+(VN2*O2z*KmDe)/(O2z*(VDe-VN2)+VDe*KmN2))*e*t','NO2')

Answer 1

[Star Strider]

To begin with, I suggest that you define the argument of ‘solve’ as a separate function (perhaps ‘polyfcn’), then do something like this:

fcn = simplify(collect(expand(polyfcn), NO2)))

That will factor out ‘NO2’ from the coefficients and simplify them, and could make your problem a bit simpler. If that fails to work, I suggest:

[polycoefs, TermsNO2] = coeffs(polyfcn, NO2)

and then see if you can solve it using the quadratic formula.