-6x2-2-3x=-8

Solution for -6x2-2-3x=-8 equation:

-6x^2-2-3x=-8

We move all terms to the left:

-6x^2-2-3x-(-8)=0

We add all the numbers together, and all the variables

-6x^2-3x+6=0

a = -6; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-6)·6
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{17}}{2*-6}=\frac{3-3\sqrt{17}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{17}}{2*-6}=\frac{3+3\sqrt{17}}{-12}
$