3/5r-3=5/r

Solution for 3/5r-3=5/r equation:

3/5r-3=5/r

We move all terms to the left:

3/5r-3-(5/r)=0


Domain of the equation: 5r!=0

r!=0/5

r!=0

r∈R



Domain of the equation: r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

3/5r-(+5/r)-3=0

We get rid of parentheses

3/5r-5/r-3=0

We calculate fractions


3r/5r^2+(-25r)/5r^2-3=0

We multiply all the terms by the denominator


3r+(-25r)-3*5r^2=0

Wy multiply elements

-15r^2+3r+(-25r)=0

We get rid of parentheses

-15r^2+3r-25r=0

We add all the numbers together, and all the variables

-15r^2-22r=0

a = -15; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-15)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-15}=\frac{0}{-30}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-15}=\frac{44}{-30}
=-1+7/15
$