r^2/5=2000

Solution for r^2/5=2000 equation:

r^2/5=2000

We move all terms to the left:

r^2/5-(2000)=0

We multiply all the terms by the denominator


r^2-2000*5=0

We add all the numbers together, and all the variables

r^2-10000=0

a = 1; b = 0; c = -10000;
Δ = b2-4ac
Δ = 02-4·1·(-10000)
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200}{2*1}=\frac{-200}{2}
=-100
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200}{2*1}=\frac{200}{2}
=100
$