3t^2-24t-15=0

Solution for 3t^2-24t-15=0 equation:

3t^2-24t-15=0

a = 3; b = -24; c = -15;
Δ = b2-4ac
Δ = -242-4·3·(-15)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{21}}{2*3}=\frac{24-6\sqrt{21}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{21}}{2*3}=\frac{24+6\sqrt{21}}{6}
$