X+2x^2-80x=180

Solution for X+2x^2-80x=180 equation:

X+2X^2-80X=180

We move all terms to the left:

X+2X^2-80X-(180)=0

We add all the numbers together, and all the variables

2X^2-79X-180=0

a = 2; b = -79; c = -180;
Δ = b2-4ac
Δ = -792-4·2·(-180)
Δ = 7681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-\sqrt{7681}}{2*2}=\frac{79-\sqrt{7681}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+\sqrt{7681}}{2*2}=\frac{79+\sqrt{7681}}{4}
$