(x+2)(x+3)=24

Solution for (x+2)(x+3)=24 equation:

(x+2)(x+3)=24

We move all terms to the left:

(x+2)(x+3)-(24)=0

We multiply parentheses ..

(+x^2+3x+2x+6)-24=0

We get rid of parentheses

x^2+3x+2x+6-24=0

We add all the numbers together, and all the variables

x^2+5x-18=0

a = 1; b = 5; c = -18;
Δ = b2-4ac
Δ = 52-4·1·(-18)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{97}}{2*1}=\frac{-5-\sqrt{97}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{97}}{2*1}=\frac{-5+\sqrt{97}}{2}
$