(X+3)(x-24)=180

Solution for (X+3)(x-24)=180 equation:

(X+3)(X-24)=180

We move all terms to the left:

(X+3)(X-24)-(180)=0

We multiply parentheses ..

(+X^2-24X+3X-72)-180=0

We get rid of parentheses

X^2-24X+3X-72-180=0

We add all the numbers together, and all the variables

X^2-21X-252=0

a = 1; b = -21; c = -252;
Δ = b2-4ac
Δ = -212-4·1·(-252)
Δ = 1449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{161}}{2*1}=\frac{21-3\sqrt{161}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{161}}{2*1}=\frac{21+3\sqrt{161}}{2}
$