3t^2-24t-21=0

Solution for 3t^2-24t-21=0 equation:

3t^2-24t-21=0

a = 3; b = -24; c = -21;
Δ = b2-4ac
Δ = -242-4·3·(-21)
Δ = 828
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:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{23}}{2*3}=\frac{24-6\sqrt{23}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{23}}{2*3}=\frac{24+6\sqrt{23}}{6}
$