3-1/2r=6-2/3r

Solution for 3-1/2r=6-2/3r equation:

3-1/2r=6-2/3r

We move all terms to the left:

3-1/2r-(6-2/3r)=0


Domain of the equation: 2r!=0

r!=0/2

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

-1/2r-(-2/3r+6)+3=0

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-18r^2+4r+(-3r)=0

We get rid of parentheses

-18r^2+4r-3r=0

We add all the numbers together, and all the variables

-18r^2+r=0

a = -18; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-18)·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*-18}=\frac{-2}{-36}
=1/18
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-18}=\frac{0}{-36}
=0
$