2x(4x+6)=48

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

2x(4x+6)=48

We move all terms to the left:

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

We multiply parentheses

8x^2+12x-48=0

a = 8; b = 12; c = -48;
Δ = b2-4ac
Δ = 122-4·8·(-48)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{105}}{2*8}=\frac{-12-4\sqrt{105}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{105}}{2*8}=\frac{-12+4\sqrt{105}}{16}
$