0=6x^2+3x-33

Solution for 0=6x^2+3x-33 equation:

0=6x^2+3x-33

We move all terms to the left:

0-(6x^2+3x-33)=0

We add all the numbers together, and all the variables

-(6x^2+3x-33)=0

We get rid of parentheses

-6x^2-3x+33=0

a = -6; b = -3; c = +33;
Δ = b2-4ac
Δ = -32-4·(-6)·33
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{89}}{2*-6}=\frac{3-3\sqrt{89}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{89}}{2*-6}=\frac{3+3\sqrt{89}}{-12}
$