1/3r+r=28

Solution for 1/3r+r=28 equation:

1/3r+r=28

We move all terms to the left:

1/3r+r-(28)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R


We add all the numbers together, and all the variables

r+1/3r-28=0

We multiply all the terms by the denominator


r*3r-28*3r+1=0

Wy multiply elements

3r^2-84r+1=0

a = 3; b = -84; c = +1;
Δ = b2-4ac
Δ = -842-4·3·1
Δ = 7044
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7044}=\sqrt{4*1761}=\sqrt{4}*\sqrt{1761}=2\sqrt{1761}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1761}}{2*3}=\frac{84-2\sqrt{1761}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1761}}{2*3}=\frac{84+2\sqrt{1761}}{6}
$