S=2n(n-1)

Solution for S=2n(n-1) equation:

=2S(S-1)

We move all terms to the left:

-(2S(S-1))=0


We calculate terms in parentheses: -(2S(S-1)), so:

2S(S-1)

We multiply parentheses

2S^2-2S

Back to the equation:

-(2S^2-2S)


We get rid of parentheses

-2S^2+2S=0

a = -2; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-2)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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