-16x^2+32x+240=x

Solution for -16x^2+32x+240=x equation:

-16x^2+32x+240=x

We move all terms to the left:

-16x^2+32x+240-(x)=0

We add all the numbers together, and all the variables

-16x^2+31x+240=0

a = -16; b = 31; c = +240;
Δ = b2-4ac
Δ = 312-4·(-16)·240
Δ = 16321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-\sqrt{16321}}{2*-16}=\frac{-31-\sqrt{16321}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{16321}}{2*-16}=\frac{-31+\sqrt{16321}}{-32}
$