-2/1r+1/3-5/2r=-25/6

Solution for -2/1r+1/3-5/2r=-25/6 equation:

-2/1r+1/3-5/2r=-25/6

We move all terms to the left:

-2/1r+1/3-5/2r-(-25/6)=0


Domain of the equation: 1r!=0

r∈R



Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R


We get rid of parentheses

-2/1r-5/2r+1/3+25/6=0

We calculate fractions


24r^2/108r^2+300r^2/108r^2+(-216r)/108r^2+(-270r)/108r^2=0

We multiply all the terms by the denominator


24r^2+300r^2+(-216r)+(-270r)=0

We add all the numbers together, and all the variables

324r^2+(-216r)+(-270r)=0

We get rid of parentheses

324r^2-216r-270r=0

We add all the numbers together, and all the variables

324r^2-486r=0

a = 324; b = -486; c = 0;
Δ = b2-4ac
Δ = -4862-4·324·0
Δ = 236196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{236196}=486$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-486)-486}{2*324}=\frac{0}{648}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-486)+486}{2*324}=\frac{972}{648}
=1+1/2
$