5(2x-2)=10x(x-2)

Solution for 5(2x-2)=10x(x-2) equation:

5(2x-2)=10x(x-2)

We move all terms to the left:

5(2x-2)-(10x(x-2))=0

We multiply parentheses

10x-(10x(x-2))-10=0


We calculate terms in parentheses: -(10x(x-2)), so:

10x(x-2)

We multiply parentheses

10x^2-20x

Back to the equation:

-(10x^2-20x)


We get rid of parentheses

-10x^2+10x+20x-10=0

We add all the numbers together, and all the variables

-10x^2+30x-10=0

a = -10; b = 30; c = -10;
Δ = b2-4ac
Δ = 302-4·(-10)·(-10)
Δ = 500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{5}}{2*-10}=\frac{-30-10\sqrt{5}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{5}}{2*-10}=\frac{-30+10\sqrt{5}}{-20}
$