3n^2=5+n

Solution for 3n^2=5+n equation:

3n^2=5+n

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

3n^2-n-5=0

We add all the numbers together, and all the variables

3n^2-1n-5=0

a = 3; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·3·(-5)
Δ = 61
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{-(-1)-\sqrt{61}}{2*3}=\frac{1-\sqrt{61}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{61}}{2*3}=\frac{1+\sqrt{61}}{6}
$