X+7=9x2-X=80

Solution for X+7=9x2-X=80 equation:

X+7=9X^2-X=80

We move all terms to the left:

X+7-(9X^2-X)=0

We get rid of parentheses

-9X^2+X+X+7=0

We add all the numbers together, and all the variables

-9X^2+2X+7=0

a = -9; b = 2; c = +7;
Δ = b2-4ac
Δ = 22-4·(-9)·7
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-16}{2*-9}=\frac{-18}{-18}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+16}{2*-9}=\frac{14}{-18}
=-7/9
$