8/3r-9/4r=-5/2

Solution for 8/3r-9/4r=-5/2 equation:

8/3r-9/4r=-5/2

We move all terms to the left:

8/3r-9/4r-(-5/2)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R



Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R


We get rid of parentheses

8/3r-9/4r+5/2=0

We calculate fractions


240r^2/48r^2+128r/48r^2+(-108r)/48r^2=0

We multiply all the terms by the denominator


240r^2+128r+(-108r)=0

We get rid of parentheses

240r^2+128r-108r=0

We add all the numbers together, and all the variables

240r^2+20r=0

a = 240; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·240·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*240}=\frac{-40}{480}
=-1/12
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*240}=\frac{0}{480}
=0
$