11000x=20000+3000x+450x^2

Solution for 11000x=20000+3000x+450x^2 equation:

11000x=20000+3000x+450x^2

We move all terms to the left:

11000x-(20000+3000x+450x^2)=0

We get rid of parentheses

-450x^2-3000x+11000x-20000=0

We add all the numbers together, and all the variables

-450x^2+8000x-20000=0

a = -450; b = 8000; c = -20000;
Δ = b2-4ac
Δ = 80002-4·(-450)·(-20000)
Δ = 28000000
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:

$\sqrt{\Delta}=\sqrt{28000000}=\sqrt{4000000*7}=\sqrt{4000000}*\sqrt{7}=2000\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8000)-2000\sqrt{7}}{2*-450}=\frac{-8000-2000\sqrt{7}}{-900}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8000)+2000\sqrt{7}}{2*-450}=\frac{-8000+2000\sqrt{7}}{-900}
$