2a-6a(a-4)=-4

Solution for 2a-6a(a-4)=-4 equation:

2a-6a(a-4)=-4

We move all terms to the left:

2a-6a(a-4)-(-4)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-6a^2+2a+24a+4=0

We add all the numbers together, and all the variables

-6a^2+26a+4=0

a = -6; b = 26; c = +4;
Δ = b2-4ac
Δ = 262-4·(-6)·4
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{193}}{2*-6}=\frac{-26-2\sqrt{193}}{-12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{193}}{2*-6}=\frac{-26+2\sqrt{193}}{-12}
$