8x-40=x(x-5)

Solution for 8x-40=x(x-5) equation:

8x-40=x(x-5)

We move all terms to the left:

8x-40-(x(x-5))=0


We calculate terms in parentheses: -(x(x-5)), so:

x(x-5)

We multiply parentheses

x^2-5x

Back to the equation:

-(x^2-5x)


We get rid of parentheses

-x^2+8x+5x-40=0

We add all the numbers together, and all the variables

-1x^2+13x-40=0

a = -1; b = 13; c = -40;
Δ = b2-4ac
Δ = 132-4·(-1)·(-40)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3}{2*-1}=\frac{-10}{-2}
=+5
$