6^-x=6^2x*1/216

Solution for 6^-x=6^2x*1/216 equation:

6^-x=6^2x*1/216

We move all terms to the left:

6^-x-(6^2x*1/216)=0

We add all the numbers together, and all the variables

-1x-(6^2x*1/216)=0

We get rid of parentheses

-1x-6^2x*1/216=0

We multiply all the terms by the denominator


-1x*216-6^2x*1=0

Wy multiply elements

-6x^2-216x=0

a = -6; b = -216; c = 0;
Δ = b2-4ac
Δ = -2162-4·(-6)·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-216}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+216}{2*-6}=\frac{432}{-12}
=-36
$