4n+2(n+1)n=52

Solution for 4n+2(n+1)n=52 equation:

4n+2(n+1)n=52

We move all terms to the left:

4n+2(n+1)n-(52)=0

We multiply parentheses

2n^2+4n+2n-52=0

We add all the numbers together, and all the variables

2n^2+6n-52=0

a = 2; b = 6; c = -52;
Δ = b2-4ac
Δ = 62-4·2·(-52)
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{113}}{2*2}=\frac{-6-2\sqrt{113}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{113}}{2*2}=\frac{-6+2\sqrt{113}}{4}
$