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

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

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

We move all terms to the left:

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


Domain of the equation: r!=0

r∈R



Domain of the equation: 3r+3)!=0

r∈R


We get rid of parentheses

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

We calculate fractions


(-9r^2)/12r^2+60r/12r^2+(-24r)/12r^2-3+1=0

We add all the numbers together, and all the variables

(-9r^2)/12r^2+60r/12r^2+(-24r)/12r^2-2=0

We multiply all the terms by the denominator


(-9r^2)+60r+(-24r)-2*12r^2=0

Wy multiply elements

(-9r^2)-24r^2+60r+(-24r)=0

We get rid of parentheses

-9r^2-24r^2+60r-24r=0

We add all the numbers together, and all the variables

-33r^2+36r=0

a = -33; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-33)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-33}=\frac{-72}{-66}
=1+1/11
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-33}=\frac{0}{-66}
=0
$