6x^2=-48x-4

Solution for 6x^2=-48x-4 equation:

6x^2=-48x-4

We move all terms to the left:

6x^2-(-48x-4)=0

We get rid of parentheses

6x^2+48x+4=0

a = 6; b = 48; c = +4;
Δ = b2-4ac
Δ = 482-4·6·4
Δ = 2208
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:

$\sqrt{\Delta}=\sqrt{2208}=\sqrt{16*138}=\sqrt{16}*\sqrt{138}=4\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{138}}{2*6}=\frac{-48-4\sqrt{138}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{138}}{2*6}=\frac{-48+4\sqrt{138}}{12}
$