3n=n^2/2

Solution for 3n=n^2/2 equation:

3n=n^2/2

We move all terms to the left:

3n-(n^2/2)=0

We get rid of parentheses

-n^2/2+3n=0

We multiply all the terms by the denominator


-n^2+3n*2=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-1n^2+6n=0

a = -1; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-1)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-1}=\frac{-12}{-2}
=+6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-1}=\frac{0}{-2}
=0
$