(3-2x)(x+2)=5

Solution for (3-2x)(x+2)=5 equation:

(3-2x)(x+2)=5

We move all terms to the left:

(3-2x)(x+2)-(5)=0

We add all the numbers together, and all the variables

(-2x+3)(x+2)-5=0

We multiply parentheses ..

(-2x^2-4x+3x+6)-5=0

We get rid of parentheses

-2x^2-4x+3x+6-5=0

We add all the numbers together, and all the variables

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

a = -2; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-2)·1
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{-(-1)-3}{2*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*-2}=\frac{4}{-4}
=-1
$