0=3x^2-18x-5

Solution for 0=3x^2-18x-5 equation:

0=3x^2-18x-5

We move all terms to the left:

0-(3x^2-18x-5)=0

We add all the numbers together, and all the variables

-(3x^2-18x-5)=0

We get rid of parentheses

-3x^2+18x+5=0

a = -3; b = 18; c = +5;
Δ = b2-4ac
Δ = 182-4·(-3)·5
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-8\sqrt{6}}{2*-3}=\frac{-18-8\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+8\sqrt{6}}{2*-3}=\frac{-18+8\sqrt{6}}{-6}
$