x^2-x-30000=0

Solution for x^2-x-30000=0 equation:

x^2-x-30000=0

We add all the numbers together, and all the variables

x^2-1x-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}
$