6t^2-12t-8=0

Solution for 6t^2-12t-8=0 equation:

6t^2-12t-8=0

a = 6; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·6·(-8)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{21}}{2*6}=\frac{12-4\sqrt{21}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{21}}{2*6}=\frac{12+4\sqrt{21}}{12}
$