2x(x+3x)=108

Solution for 2x(x+3x)=108 equation:

2x(x+3x)=108

We move all terms to the left:

2x(x+3x)-(108)=0

We add all the numbers together, and all the variables

2x(+4x)-108=0

We multiply parentheses

8x^2-108=0

a = 8; b = 0; c = -108;
Δ = b2-4ac
Δ = 02-4·8·(-108)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{6}}{2*8}=\frac{0-24\sqrt{6}}{16}
=-\frac{24\sqrt{6}}{16}
=-\frac{3\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{6}}{2*8}=\frac{0+24\sqrt{6}}{16}
=\frac{24\sqrt{6}}{16}
=\frac{3\sqrt{6}}{2}
$