1/9^2x-4=1

Solution for 1/9^2x-4=1 equation:

1/9^2x-4=1

We move all terms to the left:

1/9^2x-4-(1)=0


Domain of the equation: 9^2x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/9^2x-5=0

We multiply all the terms by the denominator


-5*9^2x+1=0

Wy multiply elements

-45x^2+1=0

a = -45; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-45)·1
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*-45}=\frac{0-6\sqrt{5}}{-90}
=-\frac{6\sqrt{5}}{-90}
=-\frac{\sqrt{5}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*-45}=\frac{0+6\sqrt{5}}{-90}
=\frac{6\sqrt{5}}{-90}
=\frac{\sqrt{5}}{-15}
$