2/3r-1/2r=-5

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

2/3r-1/2r=-5

We move all terms to the left:

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


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R



Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We add all the numbers together, and all the variables

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

We calculate fractions


4r/6r^2+(-3r)/6r^2+5=0

We multiply all the terms by the denominator


4r+(-3r)+5*6r^2=0

Wy multiply elements

30r^2+4r+(-3r)=0

We get rid of parentheses

30r^2+4r-3r=0

We add all the numbers together, and all the variables

30r^2+r=0

a = 30; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·30·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*30}=\frac{-2}{60}
=-1/30
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*30}=\frac{0}{60}
=0
$