300=n^2+n/2

Solution for 300=n^2+n/2 equation:

300=n^2+n/2

We move all terms to the left:

300-(n^2+n/2)=0

We get rid of parentheses

-n^2-n/2+300=0

We multiply all the terms by the denominator


-n^2*2-n+300*2=0

We add all the numbers together, and all the variables

-n^2*2-1n+600=0

Wy multiply elements

-2n^2-1n+600=0

a = -2; b = -1; c = +600;
Δ = b2-4ac
Δ = -12-4·(-2)·600
Δ = 4801
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{4801}}{2*-2}=\frac{1-\sqrt{4801}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{4801}}{2*-2}=\frac{1+\sqrt{4801}}{-4}
$