300x-x2=22485

Solution for 300x-x2=22485 equation:

300x-x2=22485

We move all terms to the left:

300x-x2-(22485)=0

We add all the numbers together, and all the variables

-1x^2+300x-22485=0

a = -1; b = 300; c = -22485;
Δ = b2-4ac
Δ = 3002-4·(-1)·(-22485)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-2\sqrt{15}}{2*-1}=\frac{-300-2\sqrt{15}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+2\sqrt{15}}{2*-1}=\frac{-300+2\sqrt{15}}{-2}
$