6x(4x+2)=48

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

6x(4x+2)=48

We move all terms to the left:

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

We multiply parentheses

24x^2+12x-48=0

a = 24; b = 12; c = -48;
Δ = b2-4ac
Δ = 122-4·24·(-48)
Δ = 4752
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4752}=\sqrt{144*33}=\sqrt{144}*\sqrt{33}=12\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{33}}{2*24}=\frac{-12-12\sqrt{33}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{33}}{2*24}=\frac{-12+12\sqrt{33}}{48}
$