100/r=5;r

Solution for 100/r=5;r equation:

100/r=5r

We move all terms to the left:

100/r-(5r)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

-5r+100/r=0

We multiply all the terms by the denominator


-5r*r+100=0

Wy multiply elements

-5r^2+100=0

a = -5; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-5)·100
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*-5}=\frac{0-20\sqrt{5}}{-10}
=-\frac{20\sqrt{5}}{-10}
=-\frac{2\sqrt{5}}{-1}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*-5}=\frac{0+20\sqrt{5}}{-10}
=\frac{20\sqrt{5}}{-10}
=\frac{2\sqrt{5}}{-1}
$