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

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

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

We multiply parentheses

(X-2)(2X+1)+6X+3=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2X^2+3X+1=0

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

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