5=3x^2-36x+108

Solution for 5=3x^2-36x+108 equation:

5=3x^2-36x+108

We move all terms to the left:

5-(3x^2-36x+108)=0

We get rid of parentheses

-3x^2+36x-108+5=0

We add all the numbers together, and all the variables

-3x^2+36x-103=0

a = -3; b = 36; c = -103;
Δ = b2-4ac
Δ = 362-4·(-3)·(-103)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{15}}{2*-3}=\frac{-36-2\sqrt{15}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{15}}{2*-3}=\frac{-36+2\sqrt{15}}{-6}
$