0=6x^2+10x-6

Solution for 0=6x^2+10x-6 equation:

0=6x^2+10x-6

We move all terms to the left:

0-(6x^2+10x-6)=0

We add all the numbers together, and all the variables

-(6x^2+10x-6)=0

We get rid of parentheses

-6x^2-10x+6=0

a = -6; b = -10; c = +6;
Δ = b2-4ac
Δ = -102-4·(-6)·6
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{61}}{2*-6}=\frac{10-2\sqrt{61}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{61}}{2*-6}=\frac{10+2\sqrt{61}}{-12}
$