n(n-3)/2=340

Solution for n(n-3)/2=340 equation:

n(n-3)/2=340

We move all terms to the left:

n(n-3)/2-(340)=0

We multiply all the terms by the denominator


n(n-3)-340*2=0

We add all the numbers together, and all the variables

n(n-3)-680=0

We multiply parentheses

n^2-3n-680=0

a = 1; b = -3; c = -680;
Δ = b2-4ac
Δ = -32-4·1·(-680)
Δ = 2729
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{-(-3)-\sqrt{2729}}{2*1}=\frac{3-\sqrt{2729}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{2729}}{2*1}=\frac{3+\sqrt{2729}}{2}
$