9^2x+1=87^x-2/3

Solution for 9^2x+1=87^x-2/3 equation:

9^2x+1=87^x-2/3

We move all terms to the left:

9^2x+1-(87^x-2/3)=0

We get rid of parentheses

9^2x-87^x+1+2/3=0

We multiply all the terms by the denominator


9^2x*3-87^x*3+2+1*3=0

We add all the numbers together, and all the variables

9^2x*3-87^x*3+5=0

Wy multiply elements

27x^2-261x+5=0

a = 27; b = -261; c = +5;
Δ = b2-4ac
Δ = -2612-4·27·5
Δ = 67581
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:

$\sqrt{\Delta}=\sqrt{67581}=\sqrt{9*7509}=\sqrt{9}*\sqrt{7509}=3\sqrt{7509}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-261)-3\sqrt{7509}}{2*27}=\frac{261-3\sqrt{7509}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-261)+3\sqrt{7509}}{2*27}=\frac{261+3\sqrt{7509}}{54}
$