n^2+n/2=990

Solution for n^2+n/2=990 equation:

n^2+n/2=990

We move all terms to the left:

n^2+n/2-(990)=0

We multiply all the terms by the denominator


n^2*2+n-990*2=0

We add all the numbers together, and all the variables

n^2*2+n-1980=0

Wy multiply elements

2n^2+n-1980=0

a = 2; b = 1; c = -1980;
Δ = b2-4ac
Δ = 12-4·2·(-1980)
Δ = 15841
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{15841}}{2*2}=\frac{-1-\sqrt{15841}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{15841}}{2*2}=\frac{-1+\sqrt{15841}}{4}
$