8/3r-9/4r=-52/12

Solution for 8/3r-9/4r=-52/12 equation:

8/3r-9/4r=-52/12

We move all terms to the left:

8/3r-9/4r-(-52/12)=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+52/12=0

We calculate fractions


2496r^2/144r^2+384r/144r^2+(-324r)/144r^2=0

We multiply all the terms by the denominator


2496r^2+384r+(-324r)=0

We get rid of parentheses

2496r^2+384r-324r=0

We add all the numbers together, and all the variables

2496r^2+60r=0

a = 2496; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·2496·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*2496}=\frac{-120}{4992}
=-5/208
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*2496}=\frac{0}{4992}
=0
$