-4x^2+288-24=32x

Solution for -4x^2+288-24=32x equation:

-4x^2+288-24=32x

We move all terms to the left:

-4x^2+288-24-(32x)=0

We add all the numbers together, and all the variables

-4x^2-32x+264=0

a = -4; b = -32; c = +264;
Δ = b2-4ac
Δ = -322-4·(-4)·264
Δ = 5248
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:

$\sqrt{\Delta}=\sqrt{5248}=\sqrt{64*82}=\sqrt{64}*\sqrt{82}=8\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{82}}{2*-4}=\frac{32-8\sqrt{82}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{82}}{2*-4}=\frac{32+8\sqrt{82}}{-8}
$