9x^2=1/181

Solution for 9x^2=1/181 equation:

9x^2=1/181

We move all terms to the left:

9x^2-(1/181)=0

We add all the numbers together, and all the variables

9x^2-(+1/181)=0

We get rid of parentheses

9x^2-1/181=0

We multiply all the terms by the denominator


9x^2*181-1=0

Wy multiply elements

1629x^2-1=0

a = 1629; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·1629·(-1)
Δ = 6516
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:

$\sqrt{\Delta}=\sqrt{6516}=\sqrt{36*181}=\sqrt{36}*\sqrt{181}=6\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{181}}{2*1629}=\frac{0-6\sqrt{181}}{3258}
=-\frac{6\sqrt{181}}{3258}
=-\frac{\sqrt{181}}{543}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{181}}{2*1629}=\frac{0+6\sqrt{181}}{3258}
=\frac{6\sqrt{181}}{3258}
=\frac{\sqrt{181}}{543}
$