5000(x)=-25x^2+1000x-3000

Solution for 5000(x)=-25x^2+1000x-3000 equation:

5000(x)=-25x^2+1000x-3000

We move all terms to the left:

5000(x)-(-25x^2+1000x-3000)=0

We get rid of parentheses

25x^2-1000x+5000x+3000=0

We add all the numbers together, and all the variables

25x^2+4000x+3000=0

a = 25; b = 4000; c = +3000;
Δ = b2-4ac
Δ = 40002-4·25·3000
Δ = 15700000
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:

$\sqrt{\Delta}=\sqrt{15700000}=\sqrt{10000*1570}=\sqrt{10000}*\sqrt{1570}=100\sqrt{1570}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4000)-100\sqrt{1570}}{2*25}=\frac{-4000-100\sqrt{1570}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4000)+100\sqrt{1570}}{2*25}=\frac{-4000+100\sqrt{1570}}{50}
$