S(3)=6x^2

Solution for S(3)=6x^2 equation:

(3)=6S^2

We move all terms to the left:

(3)-(6S^2)=0

a = -6; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-6)·3
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*-6}=\frac{0-6\sqrt{2}}{-12}
=-\frac{6\sqrt{2}}{-12}
=-\frac{\sqrt{2}}{-2}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*-6}=\frac{0+6\sqrt{2}}{-12}
=\frac{6\sqrt{2}}{-12}
=\frac{\sqrt{2}}{-2}
$