(x+3x)(3x)=(6+2)(6)

Solution for (x+3x)(3x)=(6+2)(6) equation:

(x+3x)(3x)=(6+2)(6)

We move all terms to the left:

(x+3x)(3x)-((6+2)(6))=0

We add all the numbers together, and all the variables

(+4x)3x-(86)=0

We add all the numbers together, and all the variables

(+4x)3x-86=0

We multiply parentheses

12x^2-86=0

a = 12; b = 0; c = -86;
Δ = b2-4ac
Δ = 02-4·12·(-86)
Δ = 4128
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:

$\sqrt{\Delta}=\sqrt{4128}=\sqrt{16*258}=\sqrt{16}*\sqrt{258}=4\sqrt{258}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{258}}{2*12}=\frac{0-4\sqrt{258}}{24}
=-\frac{4\sqrt{258}}{24}
=-\frac{\sqrt{258}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{258}}{2*12}=\frac{0+4\sqrt{258}}{24}
=\frac{4\sqrt{258}}{24}
=\frac{\sqrt{258}}{6}
$