x*x-x-3000=0

Solution for x*x-x-3000=0 equation:

x*x-x-3000=0

We add all the numbers together, and all the variables

-1x+x*x-3000=0

Wy multiply elements

x^2-1x-3000=0

a = 1; b = -1; c = -3000;
Δ = b2-4ac
Δ = -12-4·1·(-3000)
Δ = 12001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{12001}}{2*1}=\frac{1-\sqrt{12001}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{12001}}{2*1}=\frac{1+\sqrt{12001}}{2}
$