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

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

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

We move all terms to the left:

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

We multiply parentheses

10x^2-50x-(2x-10)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

10x^2-52x+10=0

a = 10; b = -52; c = +10;
Δ = b2-4ac
Δ = -522-4·10·10
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-48}{2*10}=\frac{4}{20}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+48}{2*10}=\frac{100}{20}
=5
$