r^2=1/9

Solution for r^2=1/9 equation:

r^2=1/9

We move all terms to the left:

r^2-(1/9)=0

We add all the numbers together, and all the variables

r^2-(+1/9)=0

We get rid of parentheses

r^2-1/9=0

We multiply all the terms by the denominator


r^2*9-1=0

Wy multiply elements

9r^2-1=0

a = 9; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·9·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*9}=\frac{-6}{18}
=-1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*9}=\frac{6}{18}
=1/3
$