(X+2)(2x-3)=72

Solution for (X+2)(2x-3)=72 equation:

(X+2)(2X-3)=72

We move all terms to the left:

(X+2)(2X-3)-(72)=0

We multiply parentheses ..

(+2X^2-3X+4X-6)-72=0

We get rid of parentheses

2X^2-3X+4X-6-72=0

We add all the numbers together, and all the variables

2X^2+X-78=0

a = 2; b = 1; c = -78;
Δ = b2-4ac
Δ = 12-4·2·(-78)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-25}{2*2}=\frac{-26}{4}
=-6+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+25}{2*2}=\frac{24}{4}
=6
$