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

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

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

We move all terms to the left:

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


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1170n^2+13n=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:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-1170}=\frac{-26}{-2340}
=1/90
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-1170}=\frac{0}{-2340}
=0
$