2/3r+5=2/5r-3

Solution for 2/3r+5=2/5r-3 equation:

2/3r+5=2/5r-3

We move all terms to the left:

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


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R



Domain of the equation: 5r-3)!=0

r∈R


We get rid of parentheses

2/3r-2/5r+3+5=0

We calculate fractions


10r/15r^2+(-6r)/15r^2+3+5=0

We add all the numbers together, and all the variables

10r/15r^2+(-6r)/15r^2+8=0

We multiply all the terms by the denominator


10r+(-6r)+8*15r^2=0

Wy multiply elements

120r^2+10r+(-6r)=0

We get rid of parentheses

120r^2+10r-6r=0

We add all the numbers together, and all the variables

120r^2+4r=0

a = 120; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·120·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*120}=\frac{-8}{240}
=-1/30
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*120}=\frac{0}{240}
=0
$