497000=t+0.001t^2

Solution for 497000=t+0.001t^2 equation:

497000=t+0.001t^2

We move all terms to the left:

497000-(t+0.001t^2)=0

We get rid of parentheses

-0.001t^2-t+497000=0

We add all the numbers together, and all the variables

-0.001t^2-1t+497000=0

a = -0.001; b = -1; c = +497000;
Δ = b2-4ac
Δ = -12-4·(-0.001)·497000
Δ = 1989
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1989}=\sqrt{9*221}=\sqrt{9}*\sqrt{221}=3\sqrt{221}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{221}}{2*-0.001}=\frac{1-3\sqrt{221}}{-0.002}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{221}}{2*-0.001}=\frac{1+3\sqrt{221}}{-0.002}
$