x=-x^2+34x+180

Solution for x=-x^2+34x+180 equation:

x=-x^2+34x+180

We move all terms to the left:

x-(-x^2+34x+180)=0

We get rid of parentheses

x^2-34x+x-180=0

We add all the numbers together, and all the variables

x^2-33x-180=0

a = 1; b = -33; c = -180;
Δ = b2-4ac
Δ = -332-4·1·(-180)
Δ = 1809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1809}=\sqrt{9*201}=\sqrt{9}*\sqrt{201}=3\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{201}}{2*1}=\frac{33-3\sqrt{201}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{201}}{2*1}=\frac{33+3\sqrt{201}}{2}
$