12t^2-144t-308=0

Solution for 12t^2-144t-308=0 equation:

12t^2-144t-308=0

a = 12; b = -144; c = -308;
Δ = b2-4ac
Δ = -1442-4·12·(-308)
Δ = 35520
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:

$\sqrt{\Delta}=\sqrt{35520}=\sqrt{64*555}=\sqrt{64}*\sqrt{555}=8\sqrt{555}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-8\sqrt{555}}{2*12}=\frac{144-8\sqrt{555}}{24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+8\sqrt{555}}{2*12}=\frac{144+8\sqrt{555}}{24}
$