(x-5)(x-5)(6)=384

Solution for (x-5)(x-5)(6)=384 equation:

(x-5)(x-5)(6)=384

We move all terms to the left:

(x-5)(x-5)(6)-(384)=0

We multiply parentheses ..

(+x^2-5x-5x+25)6-384=0

We multiply parentheses

6x^2-30x-30x+150-384=0

We add all the numbers together, and all the variables

6x^2-60x-234=0

a = 6; b = -60; c = -234;
Δ = b2-4ac
Δ = -602-4·6·(-234)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-96}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+96}{2*6}=\frac{156}{12}
=13
$