1/5n-3=2n

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

1/5n-3=2n

We move all terms to the left:

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


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -10; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·(-10)·1
Δ = 265
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{-(-15)-\sqrt{265}}{2*-10}=\frac{15-\sqrt{265}}{-20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{265}}{2*-10}=\frac{15+\sqrt{265}}{-20}
$