S(x)=240-8x^2

Solution for S(x)=240-8x^2 equation:

(S)=240-8S^2

We move all terms to the left:

(S)-(240-8S^2)=0

We get rid of parentheses

8S^2+S-240=0

a = 8; b = 1; c = -240;
Δ = b2-4ac
Δ = 12-4·8·(-240)
Δ = 7681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{7681}}{2*8}=\frac{-1-\sqrt{7681}}{16}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{7681}}{2*8}=\frac{-1+\sqrt{7681}}{16}
$