7/15=n2

Solution for 7/15=n2 equation:

7/15=n2

We move all terms to the left:

7/15-(n2)=0

We add all the numbers together, and all the variables

-1n^2+7/15=0

We multiply all the terms by the denominator


-1n^2*15+7=0

Wy multiply elements

-15n^2+7=0

a = -15; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-15)·7
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{105}}{2*-15}=\frac{0-2\sqrt{105}}{-30}
=-\frac{2\sqrt{105}}{-30}
=-\frac{\sqrt{105}}{-15}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{105}}{2*-15}=\frac{0+2\sqrt{105}}{-30}
=\frac{2\sqrt{105}}{-30}
=\frac{\sqrt{105}}{-15}
$