150=-16t^2+48t+288

Solution for 150=-16t^2+48t+288 equation:

150=-16t^2+48t+288

We move all terms to the left:

150-(-16t^2+48t+288)=0

We get rid of parentheses

16t^2-48t-288+150=0

We add all the numbers together, and all the variables

16t^2-48t-138=0

a = 16; b = -48; c = -138;
Δ = b2-4ac
Δ = -482-4·16·(-138)
Δ = 11136
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:

$\sqrt{\Delta}=\sqrt{11136}=\sqrt{64*174}=\sqrt{64}*\sqrt{174}=8\sqrt{174}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{174}}{2*16}=\frac{48-8\sqrt{174}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{174}}{2*16}=\frac{48+8\sqrt{174}}{32}
$