38/4=n2

Solution for 38/4=n2 equation:

38/4=n2

We move all terms to the left:

38/4-(n2)=0

We add all the numbers together, and all the variables

-1n^2+38/4=0

We multiply all the terms by the denominator


-1n^2*4+38=0

Wy multiply elements

-4n^2+38=0

a = -4; b = 0; c = +38;
Δ = b2-4ac
Δ = 02-4·(-4)·38
Δ = 608
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:

$\sqrt{\Delta}=\sqrt{608}=\sqrt{16*38}=\sqrt{16}*\sqrt{38}=4\sqrt{38}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{38}}{2*-4}=\frac{0-4\sqrt{38}}{-8}
=-\frac{4\sqrt{38}}{-8}
=-\frac{\sqrt{38}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{38}}{2*-4}=\frac{0+4\sqrt{38}}{-8}
=\frac{4\sqrt{38}}{-8}
=\frac{\sqrt{38}}{-2}
$