5(x-2)-20=-5x(x-6)

Solution for 5(x-2)-20=-5x(x-6) equation:

5(x-2)-20=-5x(x-6)

We move all terms to the left:

5(x-2)-20-(-5x(x-6))=0

We multiply parentheses

5x-(-5x(x-6))-10-20=0


We calculate terms in parentheses: -(-5x(x-6)), so:

-5x(x-6)

We multiply parentheses

-5x^2+30x

Back to the equation:

-(-5x^2+30x)


We add all the numbers together, and all the variables

-(-5x^2+30x)+5x-30=0

We get rid of parentheses

5x^2-30x+5x-30=0

We add all the numbers together, and all the variables

5x^2-25x-30=0

a = 5; b = -25; c = -30;
Δ = b2-4ac
Δ = -252-4·5·(-30)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-35}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+35}{2*5}=\frac{60}{10}
=6
$