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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(5x(x-10)), so:

5x(x-10)

We multiply parentheses

5x^2-50x

Back to the equation:

-(5x^2-50x)


We get rid of parentheses

-5x^2+5x+50x-10=0

We add all the numbers together, and all the variables

-5x^2+55x-10=0

a = -5; b = 55; c = -10;
Δ = b2-4ac
Δ = 552-4·(-5)·(-10)
Δ = 2825
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:

$\sqrt{\Delta}=\sqrt{2825}=\sqrt{25*113}=\sqrt{25}*\sqrt{113}=5\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-5\sqrt{113}}{2*-5}=\frac{-55-5\sqrt{113}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+5\sqrt{113}}{2*-5}=\frac{-55+5\sqrt{113}}{-10}
$