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

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

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

We move all terms to the left:

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

We use the square of the difference formula

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

We multiply parentheses ..

x^2-(+2x^2-4x-3x+6)-1-2=0

We add all the numbers together, and all the variables

x^2-(+2x^2-4x-3x+6)-3=0

We get rid of parentheses

x^2-2x^2+4x+3x-6-3=0

We add all the numbers together, and all the variables

-1x^2+7x-9=0

a = -1; b = 7; c = -9;
Δ = b2-4ac
Δ = 72-4·(-1)·(-9)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{13}}{2*-1}=\frac{-7-\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{13}}{2*-1}=\frac{-7+\sqrt{13}}{-2}
$