15n^2-13n-2=0

Solution for 15n^2-13n-2=0 equation:

15n^2-13n-2=0

a = 15; b = -13; c = -2;
Δ = b2-4ac
Δ = -132-4·15·(-2)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*15}=\frac{-4}{30}
=-2/15
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*15}=\frac{30}{30}
=1
$