# How to equate two equations and find one of the unknown from it as a function of second unknown?

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Kelvin Anto on 13 Dec 2021
Commented: Kelvin Anto on 13 Dec 2021
I have two equations,
R1 = 1.5;
ntone = R1 + etplusone + et; %%Equation(1)
nttwo = log(R1) + 2*etplusone + et^2; %%Equation(2)
%%% Please note, et and etplusone are the unknowns here
I wanted to equate these two equations and obtain etplusone as a function of et

Paul on 13 Dec 2021
syms et etplusone
R1 = 1.5;
ntone = R1 + etplusone + et; %%Equation(1)
nttwo = log(R1) + 2*etplusone + et^2; %%Equation(2)
soletplusone = solve(ntone == nttwo,etplusone,'ReturnConditions',true)
soletplusone = struct with fields:
etplusone: - et^2 + et + 4929346931268077/4503599627370496 parameters: [1×0 sym] conditions: symtrue
Seems like this would be straightforward to do by hand, wouldn't it?
Kelvin Anto on 13 Dec 2021
Hi Paul, Thank you for your answer. Yeah my question is actually complicated that this, but I just put an example to see the procedure.

_ on 13 Dec 2021
A little bit of algebra gives:
etplusone = - et^2 + et + R1 - log(R1);

R2020b

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