(10n)2=84

Solution for (10n)2=84 equation:

(10n)2=84

We move all terms to the left:

(10n)2-(84)=0

We add all the numbers together, and all the variables

10n^2-84=0

a = 10; b = 0; c = -84;
Δ = b2-4ac
Δ = 02-4·10·(-84)
Δ = 3360
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:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{210}}{2*10}=\frac{0-4\sqrt{210}}{20}
=-\frac{4\sqrt{210}}{20}
=-\frac{\sqrt{210}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{210}}{2*10}=\frac{0+4\sqrt{210}}{20}
=\frac{4\sqrt{210}}{20}
=\frac{\sqrt{210}}{5}
$