15n^2-17-6=0

Solution for 15n^2-17-6=0 equation:

15n^2-17-6=0

We add all the numbers together, and all the variables

15n^2-23=0

a = 15; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·15·(-23)
Δ = 1380
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:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{345}}{2*15}=\frac{0-2\sqrt{345}}{30}
=-\frac{2\sqrt{345}}{30}
=-\frac{\sqrt{345}}{15}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{345}}{2*15}=\frac{0+2\sqrt{345}}{30}
=\frac{2\sqrt{345}}{30}
=\frac{\sqrt{345}}{15}
$