500x+1300x-100x^2=4100

Solution for 500x+1300x-100x^2=4100 equation:

500x+1300x-100x^2=4100

We move all terms to the left:

500x+1300x-100x^2-(4100)=0

We add all the numbers together, and all the variables

-100x^2+1800x-4100=0

a = -100; b = 1800; c = -4100;
Δ = b2-4ac
Δ = 18002-4·(-100)·(-4100)
Δ = 1600000
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:

$\sqrt{\Delta}=\sqrt{1600000}=\sqrt{160000*10}=\sqrt{160000}*\sqrt{10}=400\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1800)-400\sqrt{10}}{2*-100}=\frac{-1800-400\sqrt{10}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1800)+400\sqrt{10}}{2*-100}=\frac{-1800+400\sqrt{10}}{-200}
$