1/4n=n-15

Solution for 1/4n=n-15 equation:

1/4n=n-15

We move all terms to the left:

1/4n-(n-15)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We get rid of parentheses

1/4n-n+15=0

We multiply all the terms by the denominator


-n*4n+15*4n+1=0

Wy multiply elements

-4n^2+60n+1=0

a = -4; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·(-4)·1
Δ = 3616
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:

$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{226}}{2*-4}=\frac{-60-4\sqrt{226}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{226}}{2*-4}=\frac{-60+4\sqrt{226}}{-8}
$