3t^2-6t-21=0

Solution for 3t^2-6t-21=0 equation:

3t^2-6t-21=0

a = 3; b = -6; c = -21;
Δ = b2-4ac
Δ = -62-4·3·(-21)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{2}}{2*3}=\frac{6-12\sqrt{2}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{2}}{2*3}=\frac{6+12\sqrt{2}}{6}
$