-2(3a-4)7a=8

Solution for -2(3a-4)7a=8 equation:

-2(3a-4)7a=8

We move all terms to the left:

-2(3a-4)7a-(8)=0

We multiply parentheses

-42a^2+56a-8=0

a = -42; b = 56; c = -8;
Δ = b2-4ac
Δ = 562-4·(-42)·(-8)
Δ = 1792
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-16\sqrt{7}}{2*-42}=\frac{-56-16\sqrt{7}}{-84}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+16\sqrt{7}}{2*-42}=\frac{-56+16\sqrt{7}}{-84}
$