5/r+5/6r=1

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

5/r+5/6r=1

We move all terms to the left:

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


Domain of the equation: r!=0

r∈R



Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R


We calculate fractions


30r/6r^2+5r/6r^2-1=0

We multiply all the terms by the denominator


30r+5r-1*6r^2=0

We add all the numbers together, and all the variables

35r-1*6r^2=0

Wy multiply elements

-6r^2+35r=0

a = -6; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-6)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-6}=\frac{-70}{-12}
=5+5/6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-6}=\frac{0}{-12}
=0
$