S(x)=(40-2x)(30-2x)

Solution for S(x)=(40-2x)(30-2x) equation:

(S)=(40-2S)(30-2S)

We move all terms to the left:

(S)-((40-2S)(30-2S))=0

We add all the numbers together, and all the variables

S-((-2S+40)(-2S+30))=0

We multiply parentheses ..

-((+4S^2-60S-80S+1200))+S=0


We calculate terms in parentheses: -((+4S^2-60S-80S+1200)), so:

(+4S^2-60S-80S+1200)

We get rid of parentheses

4S^2-60S-80S+1200

We add all the numbers together, and all the variables

4S^2-140S+1200

Back to the equation:

-(4S^2-140S+1200)


We add all the numbers together, and all the variables

S-(4S^2-140S+1200)=0

We get rid of parentheses

-4S^2+S+140S-1200=0

We add all the numbers together, and all the variables

-4S^2+141S-1200=0

a = -4; b = 141; c = -1200;
Δ = b2-4ac
Δ = 1412-4·(-4)·(-1200)
Δ = 681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(141)-\sqrt{681}}{2*-4}=\frac{-141-\sqrt{681}}{-8}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(141)+\sqrt{681}}{2*-4}=\frac{-141+\sqrt{681}}{-8}
$