-2x(3x-8)=2

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

-2x(3x-8)=2

We move all terms to the left:

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

We multiply parentheses

-6x^2+16x-2=0

a = -6; b = 16; c = -2;
Δ = b2-4ac
Δ = 162-4·(-6)·(-2)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{13}}{2*-6}=\frac{-16-4\sqrt{13}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{13}}{2*-6}=\frac{-16+4\sqrt{13}}{-12}
$