2n*5n=200

Solution for 2n*5n=200 equation:

2n*5n=200

We move all terms to the left:

2n*5n-(200)=0

Wy multiply elements

10n^2-200=0

a = 10; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·10·(-200)
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{5}}{2*10}=\frac{0-40\sqrt{5}}{20}
=-\frac{40\sqrt{5}}{20}
=-2\sqrt{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{5}}{2*10}=\frac{0+40\sqrt{5}}{20}
=\frac{40\sqrt{5}}{20}
=2\sqrt{5}
$