6^x-7/6^x=6

Solution for 6^x-7/6^x=6 equation:

6^x-7/6^x=6

We move all terms to the left:

6^x-7/6^x-(6)=0


Domain of the equation: 6^x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


6^x*6^x-6*6^x-7=0

Wy multiply elements

36x^2-36x-7=0

a = 36; b = -36; c = -7;
Δ = b2-4ac
Δ = -362-4·36·(-7)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-48}{2*36}=\frac{-12}{72}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+48}{2*36}=\frac{84}{72}
=1+1/6
$