r^2+1/5=13

Solution for r^2+1/5=13 equation:

r^2+1/5=13

We move all terms to the left:

r^2+1/5-(13)=0

determiningTheFunctionDomain
r^2-13+1/5=0

We multiply all the terms by the denominator


r^2*5+1-13*5=0

We add all the numbers together, and all the variables

r^2*5-64=0

Wy multiply elements

5r^2-64=0

a = 5; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·5·(-64)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{5}}{2*5}=\frac{0-16\sqrt{5}}{10}
=-\frac{16\sqrt{5}}{10}
=-\frac{8\sqrt{5}}{5}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{5}}{2*5}=\frac{0+16\sqrt{5}}{10}
=\frac{16\sqrt{5}}{10}
=\frac{8\sqrt{5}}{5}
$