225000=900x+9x^2

Solution for 225000=900x+9x^2 equation:

225000=900x+9x^2

We move all terms to the left:

225000-(900x+9x^2)=0

We get rid of parentheses

-9x^2-900x+225000=0

a = -9; b = -900; c = +225000;
Δ = b2-4ac
Δ = -9002-4·(-9)·225000
Δ = 8910000
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:

$\sqrt{\Delta}=\sqrt{8910000}=\sqrt{810000*11}=\sqrt{810000}*\sqrt{11}=900\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-900\sqrt{11}}{2*-9}=\frac{900-900\sqrt{11}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+900\sqrt{11}}{2*-9}=\frac{900+900\sqrt{11}}{-18}
$