2/r+2=10/3r=

Solution for 2/r+2=10/3r= equation:

2/r+2=10/3r=

We move all terms to the left:

2/r+2-(10/3r)=0


Domain of the equation: r!=0

r∈R



Domain of the equation: 3r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

2/r-(+10/3r)+2=0

We get rid of parentheses

2/r-10/3r+2=0

We calculate fractions


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

We multiply all the terms by the denominator


6r+(-10r)+2*3r^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6r^2-4r=0

a = 6; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·6·0
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*6}=\frac{0}{12}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*6}=\frac{8}{12}
=2/3
$