2a+4a(a-6)=48

Solution for 2a+4a(a-6)=48 equation:

2a+4a(a-6)=48

We move all terms to the left:

2a+4a(a-6)-(48)=0

We multiply parentheses

4a^2+2a-24a-48=0

We add all the numbers together, and all the variables

4a^2-22a-48=0

a = 4; b = -22; c = -48;
Δ = b2-4ac
Δ = -222-4·4·(-48)
Δ = 1252
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:

$\sqrt{\Delta}=\sqrt{1252}=\sqrt{4*313}=\sqrt{4}*\sqrt{313}=2\sqrt{313}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{313}}{2*4}=\frac{22-2\sqrt{313}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{313}}{2*4}=\frac{22+2\sqrt{313}}{8}
$