15n^2-n-6=0

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

15n^2-n-6=0

We add all the numbers together, and all the variables

15n^2-1n-6=0

a = 15; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·15·(-6)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*15}=\frac{-18}{30}
=-3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*15}=\frac{20}{30}
=2/3
$