3000x-x*x=100

Solution for 3000x-x*x=100 equation:

3000x-x*x=100

We move all terms to the left:

3000x-x*x-(100)=0

Wy multiply elements

-1x^2+3000x-100=0

a = -1; b = 3000; c = -100;
Δ = b2-4ac
Δ = 30002-4·(-1)·(-100)
Δ = 8999600
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:

$\sqrt{\Delta}=\sqrt{8999600}=\sqrt{400*22499}=\sqrt{400}*\sqrt{22499}=20\sqrt{22499}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3000)-20\sqrt{22499}}{2*-1}=\frac{-3000-20\sqrt{22499}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3000)+20\sqrt{22499}}{2*-1}=\frac{-3000+20\sqrt{22499}}{-2}
$