(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}
$