5n=n2+3

Solution for 5n=n2+3 equation:

5n=n2+3

We move all terms to the left:

5n-(n2+3)=0

We add all the numbers together, and all the variables

-(+n^2+3)+5n=0

We get rid of parentheses

-n^2+5n-3=0

We add all the numbers together, and all the variables

-1n^2+5n-3=0

a = -1; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·(-1)·(-3)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{13}}{2*-1}=\frac{-5-\sqrt{13}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{13}}{2*-1}=\frac{-5+\sqrt{13}}{-2}
$