r^2=134/9

Solution for r^2=134/9 equation:

r^2=134/9

We move all terms to the left:

r^2-(134/9)=0

We add all the numbers together, and all the variables

r^2-(+134/9)=0

We get rid of parentheses

r^2-134/9=0

We multiply all the terms by the denominator


r^2*9-134=0

Wy multiply elements

9r^2-134=0

a = 9; b = 0; c = -134;
Δ = b2-4ac
Δ = 02-4·9·(-134)
Δ = 4824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4824}=\sqrt{36*134}=\sqrt{36}*\sqrt{134}=6\sqrt{134}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{134}}{2*9}=\frac{0-6\sqrt{134}}{18}
=-\frac{6\sqrt{134}}{18}
=-\frac{\sqrt{134}}{3}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{134}}{2*9}=\frac{0+6\sqrt{134}}{18}
=\frac{6\sqrt{134}}{18}
=\frac{\sqrt{134}}{3}
$