1/2r+5-1/6r=21

Solution for 1/2r+5-1/6r=21 equation:

1/2r+5-1/6r=21

We move all terms to the left:

1/2r+5-1/6r-(21)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R


We add all the numbers together, and all the variables

1/2r-1/6r-16=0

We calculate fractions


6r/12r^2+(-2r)/12r^2-16=0

We multiply all the terms by the denominator


6r+(-2r)-16*12r^2=0

Wy multiply elements

-192r^2+6r+(-2r)=0

We get rid of parentheses

-192r^2+6r-2r=0

We add all the numbers together, and all the variables

-192r^2+4r=0

a = -192; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-192)·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*-192}=\frac{-8}{-384}
=1/48
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-192}=\frac{0}{-384}
=0
$