200x^2+15000x-4=73

Solution for 200x^2+15000x-4=73 equation:

200x^2+15000x-4=73

We move all terms to the left:

200x^2+15000x-4-(73)=0

We add all the numbers together, and all the variables

200x^2+15000x-77=0

a = 200; b = 15000; c = -77;
Δ = b2-4ac
Δ = 150002-4·200·(-77)
Δ = 225061600
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:

$\sqrt{\Delta}=\sqrt{225061600}=\sqrt{400*562654}=\sqrt{400}*\sqrt{562654}=20\sqrt{562654}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15000)-20\sqrt{562654}}{2*200}=\frac{-15000-20\sqrt{562654}}{400}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15000)+20\sqrt{562654}}{2*200}=\frac{-15000+20\sqrt{562654}}{400}
$