0=-4x^2-48x-141

Solution for 0=-4x^2-48x-141 equation:

0=-4x^2-48x-141

We move all terms to the left:

0-(-4x^2-48x-141)=0

We add all the numbers together, and all the variables

-(-4x^2-48x-141)=0

We get rid of parentheses

4x^2+48x+141=0

a = 4; b = 48; c = +141;
Δ = b2-4ac
Δ = 482-4·4·141
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*4}=\frac{-48-4\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{3}}{2*4}=\frac{-48+4\sqrt{3}}{8}
$