(2x-3)(3x+2)=8

Solution for (2x-3)(3x+2)=8 equation:

(2x-3)(3x+2)=8

We move all terms to the left:

(2x-3)(3x+2)-(8)=0

We multiply parentheses ..

(+6x^2+4x-9x-6)-8=0

We get rid of parentheses

6x^2+4x-9x-6-8=0

We add all the numbers together, and all the variables

6x^2-5x-14=0

a = 6; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·6·(-14)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*6}=\frac{-14}{12}
=-1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*6}=\frac{24}{12}
=2
$