96=x(20-x)

Solution for 96=x(20-x) equation:

96=x(20-x)

We move all terms to the left:

96-(x(20-x))=0

We add all the numbers together, and all the variables

-(x(-1x+20))+96=0


We calculate terms in parentheses: -(x(-1x+20)), so:

x(-1x+20)

We multiply parentheses

-1x^2+20x

Back to the equation:

-(-1x^2+20x)


We get rid of parentheses

1x^2-20x+96=0

We add all the numbers together, and all the variables

x^2-20x+96=0

a = 1; b = -20; c = +96;
Δ = b2-4ac
Δ = -202-4·1·96
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4}{2*1}=\frac{16}{2}
=8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4}{2*1}=\frac{24}{2}
=12
$