180+8x=x^2

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

180+8x=x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-x^2+8x+180=0

We add all the numbers together, and all the variables

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