5=3x^2-6x-8

Solution for 5=3x^2-6x-8 equation:

5=3x^2-6x-8

We move all terms to the left:

5-(3x^2-6x-8)=0

We get rid of parentheses

-3x^2+6x+8+5=0

We add all the numbers together, and all the variables

-3x^2+6x+13=0

a = -3; b = 6; c = +13;
Δ = b2-4ac
Δ = 62-4·(-3)·13
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-8\sqrt{3}}{2*-3}=\frac{-6-8\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+8\sqrt{3}}{2*-3}=\frac{-6+8\sqrt{3}}{-6}
$