73=4t+6t^2

Solution for 73=4t+6t^2 equation:

73=4t+6t^2

We move all terms to the left:

73-(4t+6t^2)=0

We get rid of parentheses

-6t^2-4t+73=0

a = -6; b = -4; c = +73;
Δ = b2-4ac
Δ = -42-4·(-6)·73
Δ = 1768
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:

$\sqrt{\Delta}=\sqrt{1768}=\sqrt{4*442}=\sqrt{4}*\sqrt{442}=2\sqrt{442}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{442}}{2*-6}=\frac{4-2\sqrt{442}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{442}}{2*-6}=\frac{4+2\sqrt{442}}{-12}
$