4(2a-6)a=4

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

4(2a-6)a=4

We move all terms to the left:

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

We multiply parentheses

8a^2-24a-4=0

a = 8; b = -24; c = -4;
Δ = b2-4ac
Δ = -242-4·8·(-4)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{11}}{2*8}=\frac{24-8\sqrt{11}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{11}}{2*8}=\frac{24+8\sqrt{11}}{16}
$