1/5n+7+3/7n=-10

Solution for 1/5n+7+3/7n=-10 equation:

1/5n+7+3/7n=-10

We move all terms to the left:

1/5n+7+3/7n-(-10)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 7n!=0

n!=0/7

n!=0

n∈R


We add all the numbers together, and all the variables

1/5n+3/7n+17=0

We calculate fractions


7n/35n^2+15n/35n^2+17=0

We multiply all the terms by the denominator


7n+15n+17*35n^2=0

We add all the numbers together, and all the variables

22n+17*35n^2=0

Wy multiply elements

595n^2+22n=0

a = 595; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·595·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*595}=\frac{-44}{1190}
=-22/595
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*595}=\frac{0}{1190}
=0
$