0=6x^2+2x-114

Solution for 0=6x^2+2x-114 equation:

0=6x^2+2x-114

We move all terms to the left:

0-(6x^2+2x-114)=0

We add all the numbers together, and all the variables

-(6x^2+2x-114)=0

We get rid of parentheses

-6x^2-2x+114=0

a = -6; b = -2; c = +114;
Δ = b2-4ac
Δ = -22-4·(-6)·114
Δ = 2740
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:

$\sqrt{\Delta}=\sqrt{2740}=\sqrt{4*685}=\sqrt{4}*\sqrt{685}=2\sqrt{685}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{685}}{2*-6}=\frac{2-2\sqrt{685}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{685}}{2*-6}=\frac{2+2\sqrt{685}}{-12}
$