0=6x^2-8x-18

Solution for 0=6x^2-8x-18 equation:

0=6x^2-8x-18

We move all terms to the left:

0-(6x^2-8x-18)=0

We add all the numbers together, and all the variables

-(6x^2-8x-18)=0

We get rid of parentheses

-6x^2+8x+18=0

a = -6; b = 8; c = +18;
Δ = b2-4ac
Δ = 82-4·(-6)·18
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{31}}{2*-6}=\frac{-8-4\sqrt{31}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{31}}{2*-6}=\frac{-8+4\sqrt{31}}{-12}
$