6x(2x+2)+12=50

Solution for 6x(2x+2)+12=50 equation:

6x(2x+2)+12=50

We move all terms to the left:

6x(2x+2)+12-(50)=0

We add all the numbers together, and all the variables

6x(2x+2)-38=0

We multiply parentheses

12x^2+12x-38=0

a = 12; b = 12; c = -38;
Δ = b2-4ac
Δ = 122-4·12·(-38)
Δ = 1968
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:

$\sqrt{\Delta}=\sqrt{1968}=\sqrt{16*123}=\sqrt{16}*\sqrt{123}=4\sqrt{123}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{123}}{2*12}=\frac{-12-4\sqrt{123}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{123}}{2*12}=\frac{-12+4\sqrt{123}}{24}
$