2n+6=1/5n-3

Solution for 2n+6=1/5n-3 equation:

2n+6=1/5n-3

We move all terms to the left:

2n+6-(1/5n-3)=0


Domain of the equation: 5n-3)!=0

n∈R


We get rid of parentheses

2n-1/5n+3+6=0

We multiply all the terms by the denominator


2n*5n+3*5n+6*5n-1=0

Wy multiply elements

10n^2+15n+30n-1=0

We add all the numbers together, and all the variables

10n^2+45n-1=0

a = 10; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·10·(-1)
Δ = 2065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2065}}{2*10}=\frac{-45-\sqrt{2065}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2065}}{2*10}=\frac{-45+\sqrt{2065}}{20}
$