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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-3x=0

a = 2; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·2·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*2}=\frac{6}{4}
=1+1/2
$