240=x*(x-8)

Solution for 240=x*(x-8) equation:

240=x*(x-8)

We move all terms to the left:

240-(x*(x-8))=0


We calculate terms in parentheses: -(x*(x-8)), so:

x*(x-8)

We multiply parentheses

x^2-8x

Back to the equation:

-(x^2-8x)


We get rid of parentheses

-x^2+8x+240=0

We add all the numbers together, and all the variables

-1x^2+8x+240=0

a = -1; b = 8; c = +240;
Δ = b2-4ac
Δ = 82-4·(-1)·240
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-32}{2*-1}=\frac{-40}{-2}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+32}{2*-1}=\frac{24}{-2}
=-12
$