n(.06*n)=500000.00

Solution for n(.06*n)=500000.00 equation:

n(.06n)=500000.00

We move all terms to the left:

n(.06n)-(500000.00)=0

We add all the numbers together, and all the variables

n(+.06n)-500000=0

We multiply parentheses

n^2-500000=0

a = 1; b = 0; c = -500000;
Δ = b2-4ac
Δ = 02-4·1·(-500000)
Δ = 2000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2000000}=\sqrt{1000000*2}=\sqrt{1000000}*\sqrt{2}=1000\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1000\sqrt{2}}{2*1}=\frac{0-1000\sqrt{2}}{2}
=-\frac{1000\sqrt{2}}{2}
=-500\sqrt{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1000\sqrt{2}}{2*1}=\frac{0+1000\sqrt{2}}{2}
=\frac{1000\sqrt{2}}{2}
=500\sqrt{2}
$