3/5r-1/6r-26=13

Solution for 3/5r-1/6r-26=13 equation:

3/5r-1/6r-26=13

We move all terms to the left:

3/5r-1/6r-26-(13)=0


Domain of the equation: 5r!=0

r!=0/5

r!=0

r∈R



Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R


We add all the numbers together, and all the variables

3/5r-1/6r-39=0

We calculate fractions


18r/30r^2+(-5r)/30r^2-39=0

We multiply all the terms by the denominator


18r+(-5r)-39*30r^2=0

Wy multiply elements

-1170r^2+18r+(-5r)=0

We get rid of parentheses

-1170r^2+18r-5r=0

We add all the numbers together, and all the variables

-1170r^2+13r=0

a = -1170; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-1170)·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*-1170}=\frac{-26}{-2340}
=1/90
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-1170}=\frac{0}{-2340}
=0
$