6^(2x)=512/3

Solution for 6^(2x)=512/3 equation:

6^(2x)=512/3

We move all terms to the left:

6^(2x)-(512/3)=0

We add all the numbers together, and all the variables

6^2x-(+512/3)=0

We get rid of parentheses

6^2x-512/3=0

We multiply all the terms by the denominator


6^2x*3-512=0

Wy multiply elements

18x^2-512=0

a = 18; b = 0; c = -512;
Δ = b2-4ac
Δ = 02-4·18·(-512)
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-192}{2*18}=\frac{-192}{36}
=-5+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+192}{2*18}=\frac{192}{36}
=5+1/3
$