15t^2-4t-1=0

Solution for 15t^2-4t-1=0 equation:

15t^2-4t-1=0

a = 15; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·15·(-1)
Δ = 76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{19}}{2*15}=\frac{4-2\sqrt{19}}{30}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{19}}{2*15}=\frac{4+2\sqrt{19}}{30}
$