6x(3x+6x)=21

Solution for 6x(3x+6x)=21 equation:

6x(3x+6x)=21

We move all terms to the left:

6x(3x+6x)-(21)=0

We add all the numbers together, and all the variables

6x(+9x)-21=0

We multiply parentheses

54x^2-21=0

a = 54; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·54·(-21)
Δ = 4536
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:

$\sqrt{\Delta}=\sqrt{4536}=\sqrt{324*14}=\sqrt{324}*\sqrt{14}=18\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{14}}{2*54}=\frac{0-18\sqrt{14}}{108}
=-\frac{18\sqrt{14}}{108}
=-\frac{\sqrt{14}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{14}}{2*54}=\frac{0+18\sqrt{14}}{108}
=\frac{18\sqrt{14}}{108}
=\frac{\sqrt{14}}{6}
$