2(6x^2-11x-8)=0

Solution for 2(6x^2-11x-8)=0 equation:

2(6x^2-11x-8)=0

We multiply parentheses

12x^2-22x-16=0

a = 12; b = -22; c = -16;
Δ = b2-4ac
Δ = -222-4·12·(-16)
Δ = 1252
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:

$\sqrt{\Delta}=\sqrt{1252}=\sqrt{4*313}=\sqrt{4}*\sqrt{313}=2\sqrt{313}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{313}}{2*12}=\frac{22-2\sqrt{313}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{313}}{2*12}=\frac{22+2\sqrt{313}}{24}
$