x(5x-1)-(3-2x)(5x-1)=0

Solution for x(5x-1)-(3-2x)(5x-1)=0 equation:

x(5x-1)-(3-2x)(5x-1)=0

We add all the numbers together, and all the variables

x(5x-1)-(-2x+3)(5x-1)=0

We multiply parentheses

5x^2-1x-(-2x+3)(5x-1)=0

We multiply parentheses ..

5x^2-(-10x^2+2x+15x-3)-1x=0

We get rid of parentheses

5x^2+10x^2-2x-15x-1x+3=0

We add all the numbers together, and all the variables

15x^2-18x+3=0

a = 15; b = -18; c = +3;
Δ = b2-4ac
Δ = -182-4·15·3
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12}{2*15}=\frac{6}{30}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12}{2*15}=\frac{30}{30}
=1
$