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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2+19x-4=0

a = 5; b = 19; c = -4;
Δ = b2-4ac
Δ = 192-4·5·(-4)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-21}{2*5}=\frac{-40}{10}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+21}{2*5}=\frac{2}{10}
=1/5
$