-x^2=32x+240

Solution for -x^2=32x+240 equation:

-x^2=32x+240

We move all terms to the left:

-x^2-(32x+240)=0

We add all the numbers together, and all the variables

-1x^2-(32x+240)=0

We get rid of parentheses

-1x^2-32x-240=0

a = -1; b = -32; c = -240;
Δ = b2-4ac
Δ = -322-4·(-1)·(-240)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8}{2*-1}=\frac{24}{-2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8}{2*-1}=\frac{40}{-2}
=-20
$