2=-3t^2+24t+36

Solution for 2=-3t^2+24t+36 equation:

2=-3t^2+24t+36

We move all terms to the left:

2-(-3t^2+24t+36)=0

We get rid of parentheses

3t^2-24t-36+2=0

We add all the numbers together, and all the variables

3t^2-24t-34=0

a = 3; b = -24; c = -34;
Δ = b2-4ac
Δ = -242-4·3·(-34)
Δ = 984
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:

$\sqrt{\Delta}=\sqrt{984}=\sqrt{4*246}=\sqrt{4}*\sqrt{246}=2\sqrt{246}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{246}}{2*3}=\frac{24-2\sqrt{246}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{246}}{2*3}=\frac{24+2\sqrt{246}}{6}
$