3/5r=3/6r+3

Solution for 3/5r=3/6r+3 equation:

3/5r=3/6r+3

We move all terms to the left:

3/5r-(3/6r+3)=0


Domain of the equation: 5r!=0

r!=0/5

r!=0

r∈R



Domain of the equation: 6r+3)!=0

r∈R


We get rid of parentheses

3/5r-3/6r-3=0

We calculate fractions


18r/30r^2+(-15r)/30r^2-3=0

We multiply all the terms by the denominator


18r+(-15r)-3*30r^2=0

Wy multiply elements

-90r^2+18r+(-15r)=0

We get rid of parentheses

-90r^2+18r-15r=0

We add all the numbers together, and all the variables

-90r^2+3r=0

a = -90; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-90)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-90}=\frac{-6}{-180}
=1/30
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-90}=\frac{0}{-180}
=0
$