10,000+5000x=500(x)^2

Solution for 10,000+5000x=500(x)^2 equation:

10.000+5000x=500(x)^2

We move all terms to the left:

10.000+5000x-(500(x)^2)=0

determiningTheFunctionDomain
5000x-500x^2+10.000=0

We add all the numbers together, and all the variables

-500x^2+5000x+10.000=0

We add all the numbers together, and all the variables

-500x^2+5000x+10=0

a = -500; b = 5000; c = +10;
Δ = b2-4ac
Δ = 50002-4·(-500)·10
Δ = 25020000
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:

$\sqrt{\Delta}=\sqrt{25020000}=\sqrt{90000*278}=\sqrt{90000}*\sqrt{278}=300\sqrt{278}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5000)-300\sqrt{278}}{2*-500}=\frac{-5000-300\sqrt{278}}{-1000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5000)+300\sqrt{278}}{2*-500}=\frac{-5000+300\sqrt{278}}{-1000}
$