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

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

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

We move all terms to the left:

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

We multiply parentheses

-3a^2+4a+12a-8=0

We add all the numbers together, and all the variables

-3a^2+16a-8=0

a = -3; b = 16; c = -8;
Δ = b2-4ac
Δ = 162-4·(-3)·(-8)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{10}}{2*-3}=\frac{-16-4\sqrt{10}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{10}}{2*-3}=\frac{-16+4\sqrt{10}}{-6}
$