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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-3x-3=0

a = 2; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·2·(-3)
Δ = 33
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{-(-3)-\sqrt{33}}{2*2}=\frac{3-\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*2}=\frac{3+\sqrt{33}}{4}
$