0=6x^2-8x-11

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

0=6x^2-8x-11

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-6x^2+8x+11=0

a = -6; b = 8; c = +11;
Δ = b2-4ac
Δ = 82-4·(-6)·11
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{82}}{2*-6}=\frac{-8-2\sqrt{82}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{82}}{2*-6}=\frac{-8+2\sqrt{82}}{-12}
$