1/3r=r-20

Solution for 1/3r=r-20 equation:

1/3r=r-20

We move all terms to the left:

1/3r-(r-20)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We get rid of parentheses

1/3r-r+20=0

We multiply all the terms by the denominator


-r*3r+20*3r+1=0

Wy multiply elements

-3r^2+60r+1=0

a = -3; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·(-3)·1
Δ = 3612
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:

$\sqrt{\Delta}=\sqrt{3612}=\sqrt{4*903}=\sqrt{4}*\sqrt{903}=2\sqrt{903}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-2\sqrt{903}}{2*-3}=\frac{-60-2\sqrt{903}}{-6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+2\sqrt{903}}{2*-3}=\frac{-60+2\sqrt{903}}{-6}
$