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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(5x(2x-2)), so:

5x(2x-2)

We multiply parentheses

10x^2-10x

Back to the equation:

-(10x^2-10x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-10x^2+11x+10=0

a = -10; b = 11; c = +10;
Δ = b2-4ac
Δ = 112-4·(-10)·10
Δ = 521
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{-(11)-\sqrt{521}}{2*-10}=\frac{-11-\sqrt{521}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{521}}{2*-10}=\frac{-11+\sqrt{521}}{-20}
$