-2x^2=40x+72

Solution for -2x^2=40x+72 equation:

-2x^2=40x+72

We move all terms to the left:

-2x^2-(40x+72)=0

We get rid of parentheses

-2x^2-40x-72=0

a = -2; b = -40; c = -72;
Δ = b2-4ac
Δ = -402-4·(-2)·(-72)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-32}{2*-2}=\frac{8}{-4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+32}{2*-2}=\frac{72}{-4}
=-18
$