-6x(x+7)=-12

Solution for -6x(x+7)=-12 equation:

-6x(x+7)=-12

We move all terms to the left:

-6x(x+7)-(-12)=0

We add all the numbers together, and all the variables

-6x(x+7)+12=0

We multiply parentheses

-6x^2-42x+12=0

a = -6; b = -42; c = +12;
Δ = b2-4ac
Δ = -422-4·(-6)·12
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{57}}{2*-6}=\frac{42-6\sqrt{57}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{57}}{2*-6}=\frac{42+6\sqrt{57}}{-12}
$