(X-5)(x+3)2=120

Solution for (X-5)(x+3)2=120 equation:

(X-5)(X+3)2=120

We move all terms to the left:

(X-5)(X+3)2-(120)=0

We multiply parentheses ..

(+X^2+3X-5X-15)2-120=0

We multiply parentheses

2X^2+6X-10X-30-120=0

We add all the numbers together, and all the variables

2X^2-4X-150=0

a = 2; b = -4; c = -150;
Δ = b2-4ac
Δ = -42-4·2·(-150)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{19}}{2*2}=\frac{4-8\sqrt{19}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{19}}{2*2}=\frac{4+8\sqrt{19}}{4}
$