2(x^2-12x-4)1/2-3=15

Solution for 2(x^2-12x-4)1/2-3=15 equation:

2(x^2-12x-4)1/2-3=15

We move all terms to the left:

2(x^2-12x-4)1/2-3-(15)=0

We add all the numbers together, and all the variables

2(x^2-12x-4)1/2-18=0

We multiply all the terms by the denominator


2(x^2-12x-4)1-18*2=0

We add all the numbers together, and all the variables

2(x^2-12x-4)1-36=0

We multiply parentheses

2x^2-24x-8-36=0

We add all the numbers together, and all the variables

2x^2-24x-44=0

a = 2; b = -24; c = -44;
Δ = b2-4ac
Δ = -242-4·2·(-44)
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{58}}{2*2}=\frac{24-4\sqrt{58}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{58}}{2*2}=\frac{24+4\sqrt{58}}{4}
$