3n*3n=38

Solution for 3n*3n=38 equation:

3n*3n=38

We move all terms to the left:

3n*3n-(38)=0

Wy multiply elements

9n^2-38=0

a = 9; b = 0; c = -38;
Δ = b2-4ac
Δ = 02-4·9·(-38)
Δ = 1368
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:

$\sqrt{\Delta}=\sqrt{1368}=\sqrt{36*38}=\sqrt{36}*\sqrt{38}=6\sqrt{38}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{38}}{2*9}=\frac{0-6\sqrt{38}}{18}
=-\frac{6\sqrt{38}}{18}
=-\frac{\sqrt{38}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{38}}{2*9}=\frac{0+6\sqrt{38}}{18}
=\frac{6\sqrt{38}}{18}
=\frac{\sqrt{38}}{3}
$