(3/r)+(3/7r)=1

Solution for (3/r)+(3/7r)=1 equation:

(3/r)+(3/7r)=1

We move all terms to the left:

(3/r)+(3/7r)-(1)=0


Domain of the equation: r)!=0

r!=0/1

r!=0

r∈R



Domain of the equation: 7r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

(+3/r)+(+3/7r)-1=0

We get rid of parentheses

3/r+3/7r-1=0

We calculate fractions


21r/7r^2+3r/7r^2-1=0

We multiply all the terms by the denominator


21r+3r-1*7r^2=0

We add all the numbers together, and all the variables

24r-1*7r^2=0

Wy multiply elements

-7r^2+24r=0

a = -7; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-7)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-7}=\frac{-48}{-14}
=3+3/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-7}=\frac{0}{-14}
=0
$