3t^2-2t-27=0

Solution for 3t^2-2t-27=0 equation:

3t^2-2t-27=0

a = 3; b = -2; c = -27;
Δ = b2-4ac
Δ = -22-4·3·(-27)
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{82}}{2*3}=\frac{2-2\sqrt{82}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{82}}{2*3}=\frac{2+2\sqrt{82}}{6}
$