X(x+1)=30000

Solution for X(x+1)=30000 equation:

X(X+1)=30000

We move all terms to the left:

X(X+1)-(30000)=0

We multiply parentheses

X^2+X-30000=0

a = 1; b = 1; c = -30000;
Δ = b2-4ac
Δ = 12-4·1·(-30000)
Δ = 120001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120001}=\sqrt{49*2449}=\sqrt{49}*\sqrt{2449}=7\sqrt{2449}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7\sqrt{2449}}{2*1}=\frac{-1-7\sqrt{2449}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7\sqrt{2449}}{2*1}=\frac{-1+7\sqrt{2449}}{2}
$