x^2=8x+180

Solution for x^2=8x+180 equation:

x^2=8x+180

We move all terms to the left:

x^2-(8x+180)=0

We get rid of parentheses

x^2-8x-180=0

a = 1; b = -8; c = -180;
Δ = b2-4ac
Δ = -82-4·1·(-180)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-28}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+28}{2*1}=\frac{36}{2}
=18
$