2/r+5/3r=1

Solution for 2/r+5/3r=1 equation:

2/r+5/3r=1

We move all terms to the left:

2/r+5/3r-(1)=0


Domain of the equation: r!=0

r∈R



Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We calculate fractions


6r/3r^2+5r/3r^2-1=0

We multiply all the terms by the denominator


6r+5r-1*3r^2=0

We add all the numbers together, and all the variables

11r-1*3r^2=0

Wy multiply elements

-3r^2+11r=0

a = -3; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-3)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-3}=\frac{-22}{-6}
=3+2/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-3}=\frac{0}{-6}
=0
$