300x-x2=6400

Solution for 300x-x2=6400 equation:

300x-x2=6400

We move all terms to the left:

300x-x2-(6400)=0

We add all the numbers together, and all the variables

-1x^2+300x-6400=0

a = -1; b = 300; c = -6400;
Δ = b2-4ac
Δ = 3002-4·(-1)·(-6400)
Δ = 64400
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:

$\sqrt{\Delta}=\sqrt{64400}=\sqrt{400*161}=\sqrt{400}*\sqrt{161}=20\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-20\sqrt{161}}{2*-1}=\frac{-300-20\sqrt{161}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+20\sqrt{161}}{2*-1}=\frac{-300+20\sqrt{161}}{-2}
$