n(4n+n)=39

Solution for n(4n+n)=39 equation:

n(4n+n)=39

We move all terms to the left:

n(4n+n)-(39)=0

We add all the numbers together, and all the variables

n(+5n)-39=0

We multiply parentheses

5n^2-39=0

a = 5; b = 0; c = -39;
Δ = b2-4ac
Δ = 02-4·5·(-39)
Δ = 780
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:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{195}}{2*5}=\frac{0-2\sqrt{195}}{10}
=-\frac{2\sqrt{195}}{10}
=-\frac{\sqrt{195}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{195}}{2*5}=\frac{0+2\sqrt{195}}{10}
=\frac{2\sqrt{195}}{10}
=\frac{\sqrt{195}}{5}
$