5x(x-4)-10=5(x-8)

Solution for 5x(x-4)-10=5(x-8) equation:

5x(x-4)-10=5(x-8)

We move all terms to the left:

5x(x-4)-10-(5(x-8))=0

We multiply parentheses

5x^2-20x-(5(x-8))-10=0


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

5(x-8)

We multiply parentheses

5x-40

Back to the equation:

-(5x-40)


We get rid of parentheses

5x^2-20x-5x+40-10=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 = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5}{2*5}=\frac{20}{10}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5}{2*5}=\frac{30}{10}
=3
$