r+3r=52/r

Solution for r+3r=52/r equation:

r+3r=52/r

We move all terms to the left:

r+3r-(52/r)=0


Domain of the equation: r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

r+3r-(+52/r)=0

We add all the numbers together, and all the variables

4r-(+52/r)=0

We get rid of parentheses

4r-52/r=0

We multiply all the terms by the denominator


4r*r-52=0

Wy multiply elements

4r^2-52=0

a = 4; b = 0; c = -52;
Δ = b2-4ac
Δ = 02-4·4·(-52)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{13}}{2*4}=\frac{0-8\sqrt{13}}{8}
=-\frac{8\sqrt{13}}{8}
=-\sqrt{13}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{13}}{2*4}=\frac{0+8\sqrt{13}}{8}
=\frac{8\sqrt{13}}{8}
=\sqrt{13}
$