n(n-1)=34782

Solution for n(n-1)=34782 equation:

n(n-1)=34782

We move all terms to the left:

n(n-1)-(34782)=0

We multiply parentheses

n^2-1n-34782=0

a = 1; b = -1; c = -34782;
Δ = b2-4ac
Δ = -12-4·1·(-34782)
Δ = 139129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{139129}=373$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-373}{2*1}=\frac{-372}{2}
=-186
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+373}{2*1}=\frac{374}{2}
=187
$