1/7r+1/6r=13

Solution for 1/7r+1/6r=13 equation:

1/7r+1/6r=13

We move all terms to the left:

1/7r+1/6r-(13)=0


Domain of the equation: 7r!=0

r!=0/7

r!=0

r∈R



Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R


We calculate fractions


6r/42r^2+7r/42r^2-13=0

We multiply all the terms by the denominator


6r+7r-13*42r^2=0

We add all the numbers together, and all the variables

13r-13*42r^2=0

Wy multiply elements

-546r^2+13r=0

a = -546; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-546)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-546}=\frac{-26}{-1092}
=1/42
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-546}=\frac{0}{-1092}
=0
$