(2x+3)(x-2)=9

Solution for (2x+3)(x-2)=9 equation:

(2x+3)(x-2)=9

We move all terms to the left:

(2x+3)(x-2)-(9)=0

We multiply parentheses ..

(+2x^2-4x+3x-6)-9=0

We get rid of parentheses

2x^2-4x+3x-6-9=0

We add all the numbers together, and all the variables

2x^2-1x-15=0

a = 2; b = -1; c = -15;
Δ = b2-4ac
Δ = -12-4·2·(-15)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*2}=\frac{12}{4}
=3
$