(2/3)^x=91x

Solution for (2/3)^x=91x equation:

(2/3)^x=91x

We move all terms to the left:

(2/3)^x-(91x)=0


Domain of the equation: 3)^x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/3)^x-91x=0

We add all the numbers together, and all the variables

-91x+(+2/3)^x=0

We multiply all the terms by the denominator


-91x*3)^x+(+2=0

Wy multiply elements

-273x^2+2=0

a = -273; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-273)·2
Δ = 2184
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:

$\sqrt{\Delta}=\sqrt{2184}=\sqrt{4*546}=\sqrt{4}*\sqrt{546}=2\sqrt{546}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{546}}{2*-273}=\frac{0-2\sqrt{546}}{-546}
=-\frac{2\sqrt{546}}{-546}
=-\frac{\sqrt{546}}{-273}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{546}}{2*-273}=\frac{0+2\sqrt{546}}{-546}
=\frac{2\sqrt{546}}{-546}
=\frac{\sqrt{546}}{-273}
$