(4a-4)a=6

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

(4a-4)a=6

We move all terms to the left:

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

We multiply parentheses

4a^2-4a-6=0

a = 4; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·4·(-6)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*4}=\frac{4-4\sqrt{7}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*4}=\frac{4+4\sqrt{7}}{8}
$