0=3x^2-2x-18

Solution for 0=3x^2-2x-18 equation:

0=3x^2-2x-18

We move all terms to the left:

0-(3x^2-2x-18)=0

We add all the numbers together, and all the variables

-(3x^2-2x-18)=0

We get rid of parentheses

-3x^2+2x+18=0

a = -3; b = 2; c = +18;
Δ = b2-4ac
Δ = 22-4·(-3)·18
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{55}}{2*-3}=\frac{-2-2\sqrt{55}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{55}}{2*-3}=\frac{-2+2\sqrt{55}}{-6}
$