x-20=-5x(x-8)

Solution for x-20=-5x(x-8) equation:

x-20=-5x(x-8)

We move all terms to the left:

x-20-(-5x(x-8))=0


We calculate terms in parentheses: -(-5x(x-8)), so:

-5x(x-8)

We multiply parentheses

-5x^2+40x

Back to the equation:

-(-5x^2+40x)


We get rid of parentheses

5x^2-40x+x-20=0

We add all the numbers together, and all the variables

5x^2-39x-20=0

a = 5; b = -39; c = -20;
Δ = b2-4ac
Δ = -392-4·5·(-20)
Δ = 1921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1921}}{2*5}=\frac{39-\sqrt{1921}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1921}}{2*5}=\frac{39+\sqrt{1921}}{10}
$