n(n-3)/2=434

Solution for n(n-3)/2=434 equation:

n(n-3)/2=434

We move all terms to the left:

n(n-3)/2-(434)=0

We multiply all the terms by the denominator


n(n-3)-434*2=0

We add all the numbers together, and all the variables

n(n-3)-868=0

We multiply parentheses

n^2-3n-868=0

a = 1; b = -3; c = -868;
Δ = b2-4ac
Δ = -32-4·1·(-868)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-59}{2*1}=\frac{-56}{2}
=-28
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+59}{2*1}=\frac{62}{2}
=31
$