24n^2-2n-1=0

Solution for 24n^2-2n-1=0 equation:

24n^2-2n-1=0

a = 24; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·24·(-1)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*24}=\frac{-8}{48}
=-1/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*24}=\frac{12}{48}
=1/4
$