6x+2x(-4)x=-6

Solution for 6x+2x(-4)x=-6 equation:

6x+2x(-4)x=-6

We move all terms to the left:

6x+2x(-4)x-(-6)=0

We add all the numbers together, and all the variables

6x+2x(-4)x+6=0

We multiply parentheses

-8x^2+6x+6=0

a = -8; b = 6; c = +6;
Δ = b2-4ac
Δ = 62-4·(-8)·6
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{57}}{2*-8}=\frac{-6-2\sqrt{57}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{57}}{2*-8}=\frac{-6+2\sqrt{57}}{-16}
$