1/2r-2/3r=7/12

Solution for 1/2r-2/3r=7/12 equation:

1/2r-2/3r=7/12

We move all terms to the left:

1/2r-2/3r-(7/12)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We add all the numbers together, and all the variables

1/2r-2/3r-(+7/12)=0

We get rid of parentheses

1/2r-2/3r-7/12=0

We calculate fractions


(-126r^2)/72r^2+36r/72r^2+(-48r)/72r^2=0

We multiply all the terms by the denominator


(-126r^2)+36r+(-48r)=0

We get rid of parentheses

-126r^2+36r-48r=0

We add all the numbers together, and all the variables

-126r^2-12r=0

a = -126; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-126)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-126}=\frac{0}{-252}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-126}=\frac{24}{-252}
=-2/21
$