2*3^2x/7=30

Solution for 2*3^2x/7=30 equation:

2*3^2x/7=30

We move all terms to the left:

2*3^2x/7-(30)=0

We multiply all the terms by the denominator


2*3^2x-30*7=0

We add all the numbers together, and all the variables

2*3^2x-210=0

Wy multiply elements

6x^2-210=0

a = 6; b = 0; c = -210;
Δ = b2-4ac
Δ = 02-4·6·(-210)
Δ = 5040
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:

$\sqrt{\Delta}=\sqrt{5040}=\sqrt{144*35}=\sqrt{144}*\sqrt{35}=12\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{35}}{2*6}=\frac{0-12\sqrt{35}}{12}
=-\frac{12\sqrt{35}}{12}
=-\sqrt{35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{35}}{2*6}=\frac{0+12\sqrt{35}}{12}
=\frac{12\sqrt{35}}{12}
=\sqrt{35}
$