21/2r-12/3r=5/12

Solution for 21/2r-12/3r=5/12 equation:

21/2r-12/3r=5/12

We move all terms to the left:

21/2r-12/3r-(5/12)=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

21/2r-12/3r-(+5/12)=0

We get rid of parentheses

21/2r-12/3r-5/12=0

We calculate fractions


(-90r^2)/72r^2+756r/72r^2+(-288r)/72r^2=0

We multiply all the terms by the denominator


(-90r^2)+756r+(-288r)=0

We get rid of parentheses

-90r^2+756r-288r=0

We add all the numbers together, and all the variables

-90r^2+468r=0

a = -90; b = 468; c = 0;
Δ = b2-4ac
Δ = 4682-4·(-90)·0
Δ = 219024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{219024}=468$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(468)-468}{2*-90}=\frac{-936}{-180}
=5+1/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(468)+468}{2*-90}=\frac{0}{-180}
=0
$