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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

(+2x^2+6x-1x-3)-x+1=0

We add all the numbers together, and all the variables

(+2x^2+6x-1x-3)-1x+1=0

We get rid of parentheses

2x^2+6x-1x-1x-3+1=0

We add all the numbers together, and all the variables

2x^2+4x-2=0

a = 2; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·2·(-2)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*2}=\frac{-4-4\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*2}=\frac{-4+4\sqrt{2}}{4}
$