X^2+71=81x-9

Solution for X^2+71=81x-9 equation:

X^2+71=81X-9

We move all terms to the left:

X^2+71-(81X-9)=0

We get rid of parentheses

X^2-81X+9+71=0

We add all the numbers together, and all the variables

X^2-81X+80=0

a = 1; b = -81; c = +80;
Δ = b2-4ac
Δ = -812-4·1·80
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-79}{2*1}=\frac{2}{2}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+79}{2*1}=\frac{160}{2}
=80
$