1/2n+3=47n+3

Solution for 1/2n+3=47n+3 equation:

1/2n+3=47n+3

We move all terms to the left:

1/2n+3-(47n+3)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

1/2n-47n-3+3=0

We multiply all the terms by the denominator


-47n*2n-3*2n+3*2n+1=0

Wy multiply elements

-94n^2-6n+6n+1=0

We add all the numbers together, and all the variables

-94n^2+1=0

a = -94; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-94)·1
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{94}}{2*-94}=\frac{0-2\sqrt{94}}{-188}
=-\frac{2\sqrt{94}}{-188}
=-\frac{\sqrt{94}}{-94}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{94}}{2*-94}=\frac{0+2\sqrt{94}}{-188}
=\frac{2\sqrt{94}}{-188}
=\frac{\sqrt{94}}{-94}
$