S^3-5s^2=36s

Solution for S^3-5s^2=36s equation:

^3-5S^2=36S

We move all terms to the left:

^3-5S^2-(36S)=0

We add all the numbers together, and all the variables

-5S^2-36S=0

a = -5; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·(-5)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*-5}=\frac{0}{-10}
=0
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*-5}=\frac{72}{-10}
=-7+1/5
$