15n^2-15n-6=0

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

15n^2-15n-6=0

a = 15; b = -15; c = -6;
Δ = b2-4ac
Δ = -152-4·15·(-6)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{65}}{2*15}=\frac{15-3\sqrt{65}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{65}}{2*15}=\frac{15+3\sqrt{65}}{30}
$