-3x^2+48x-180=8

Solution for -3x^2+48x-180=8 equation:

-3x^2+48x-180=8

We move all terms to the left:

-3x^2+48x-180-(8)=0

We add all the numbers together, and all the variables

-3x^2+48x-188=0

a = -3; b = 48; c = -188;
Δ = b2-4ac
Δ = 482-4·(-3)·(-188)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{3}}{2*-3}=\frac{-48-4\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{3}}{2*-3}=\frac{-48+4\sqrt{3}}{-6}
$