2n+13/4n=60

Solution for 2n+13/4n=60 equation:

2n+13/4n=60

We move all terms to the left:

2n+13/4n-(60)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We multiply all the terms by the denominator


2n*4n-60*4n+13=0

Wy multiply elements

8n^2-240n+13=0

a = 8; b = -240; c = +13;
Δ = b2-4ac
Δ = -2402-4·8·13
Δ = 57184
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:

$\sqrt{\Delta}=\sqrt{57184}=\sqrt{16*3574}=\sqrt{16}*\sqrt{3574}=4\sqrt{3574}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-4\sqrt{3574}}{2*8}=\frac{240-4\sqrt{3574}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+4\sqrt{3574}}{2*8}=\frac{240+4\sqrt{3574}}{16}
$