S^2-2s^2-48s=0

Solution for S^2-2s^2-48s=0 equation:

^2-2S^2-48S=0

We add all the numbers together, and all the variables

-2S^2-48S=0

a = -2; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·(-2)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*-2}=\frac{0}{-4}
=0
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*-2}=\frac{96}{-4}
=-24
$