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

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

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

We move all terms to the left:

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


Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R



Domain of the equation: 2r+2)!=0

r∈R


We get rid of parentheses

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

We calculate fractions


2r/12r^2+(-6r)/12r^2-2-5=0

We add all the numbers together, and all the variables

2r/12r^2+(-6r)/12r^2-7=0

We multiply all the terms by the denominator


2r+(-6r)-7*12r^2=0

Wy multiply elements

-84r^2+2r+(-6r)=0

We get rid of parentheses

-84r^2+2r-6r=0

We add all the numbers together, and all the variables

-84r^2-4r=0

a = -84; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-84)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-84}=\frac{0}{-168}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-84}=\frac{8}{-168}
=-1/21
$