2x(3x-8)=-6

Solution for 2x(3x-8)=-6 equation:

2x(3x-8)=-6

We move all terms to the left:

2x(3x-8)-(-6)=0

We add all the numbers together, and all the variables

2x(3x-8)+6=0

We multiply parentheses

6x^2-16x+6=0

a = 6; b = -16; c = +6;
Δ = b2-4ac
Δ = -162-4·6·6
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{7}}{2*6}=\frac{16-4\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{7}}{2*6}=\frac{16+4\sqrt{7}}{12}
$