-3t^2+30t+73=0

Solution for -3t^2+30t+73=0 equation:

-3t^2+30t+73=0

a = -3; b = 30; c = +73;
Δ = b2-4ac
Δ = 302-4·(-3)·73
Δ = 1776
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:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-4\sqrt{111}}{2*-3}=\frac{-30-4\sqrt{111}}{-6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+4\sqrt{111}}{2*-3}=\frac{-30+4\sqrt{111}}{-6}
$