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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2+5X-66=0

a = 1; b = 5; c = -66;
Δ = b2-4ac
Δ = 52-4·1·(-66)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-17}{2*1}=\frac{-22}{2}
=-11
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+17}{2*1}=\frac{12}{2}
=6
$