S1=x(60-2x)

Solution for S1=x(60-2x) equation:

1=S(60-2S)

We move all terms to the left:

1-(S(60-2S))=0

We add all the numbers together, and all the variables

-(S(-2S+60))+1=0


We calculate terms in parentheses: -(S(-2S+60)), so:

S(-2S+60)

We multiply parentheses

-2S^2+60S

Back to the equation:

-(-2S^2+60S)


We get rid of parentheses

2S^2-60S+1=0

a = 2; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·2·1
Δ = 3592
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:

$\sqrt{\Delta}=\sqrt{3592}=\sqrt{4*898}=\sqrt{4}*\sqrt{898}=2\sqrt{898}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{898}}{2*2}=\frac{60-2\sqrt{898}}{4}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{898}}{2*2}=\frac{60+2\sqrt{898}}{4}
$