1/5n+-15n=0

Solution for 1/5n+-15n=0 equation:

1/5n+-15n=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

-15n+1/5n=0

We multiply all the terms by the denominator


-15n*5n+1=0

Wy multiply elements

-75n^2+1=0

a = -75; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-75)·1
Δ = 300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*-75}=\frac{0-10\sqrt{3}}{-150}
=-\frac{10\sqrt{3}}{-150}
=-\frac{\sqrt{3}}{-15}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*-75}=\frac{0+10\sqrt{3}}{-150}
=\frac{10\sqrt{3}}{-150}
=\frac{\sqrt{3}}{-15}
$