150=-16t^2+120t+6

Solution for 150=-16t^2+120t+6 equation:

150=-16t^2+120t+6

We move all terms to the left:

150-(-16t^2+120t+6)=0

We get rid of parentheses

16t^2-120t-6+150=0

We add all the numbers together, and all the variables

16t^2-120t+144=0

a = 16; b = -120; c = +144;
Δ = b2-4ac
Δ = -1202-4·16·144
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-72}{2*16}=\frac{48}{32}
=1+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+72}{2*16}=\frac{192}{32}
=6
$