200x^2+15000x-x=73

Solution for 200x^2+15000x-x=73 equation:

200x^2+15000x-x=73

We move all terms to the left:

200x^2+15000x-x-(73)=0

We add all the numbers together, and all the variables

200x^2+14999x-73=0

a = 200; b = 14999; c = -73;
Δ = b2-4ac
Δ = 149992-4·200·(-73)
Δ = 225028401
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:

$\sqrt{\Delta}=\sqrt{225028401}=\sqrt{169*1331529}=\sqrt{169}*\sqrt{1331529}=13\sqrt{1331529}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14999)-13\sqrt{1331529}}{2*200}=\frac{-14999-13\sqrt{1331529}}{400}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14999)+13\sqrt{1331529}}{2*200}=\frac{-14999+13\sqrt{1331529}}{400}
$