-6x(x+7)-6=-48

Solution for -6x(x+7)-6=-48 equation:

-6x(x+7)-6=-48

We move all terms to the left:

-6x(x+7)-6-(-48)=0

We add all the numbers together, and all the variables

-6x(x+7)+42=0

We multiply parentheses

-6x^2-42x+42=0

a = -6; b = -42; c = +42;
Δ = b2-4ac
Δ = -422-4·(-6)·42
Δ = 2772
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:

$\sqrt{\Delta}=\sqrt{2772}=\sqrt{36*77}=\sqrt{36}*\sqrt{77}=6\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{77}}{2*-6}=\frac{42-6\sqrt{77}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{77}}{2*-6}=\frac{42+6\sqrt{77}}{-12}
$