15n2-n=2

Solution for 15n2-n=2 equation:

15n^2-n=2

We move all terms to the left:

15n^2-n-(2)=0

We add all the numbers together, and all the variables

15n^2-1n-2=0

a = 15; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·15·(-2)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*15}=\frac{-10}{30}
=-1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*15}=\frac{12}{30}
=2/5
$