Y=300+150t-16t^2

Solution for Y=300+150t-16t^2 equation:

=300+150Y-16Y^2

We move all terms to the left:

-(300+150Y-16Y^2)=0

We get rid of parentheses

16Y^2-150Y-300=0

a = 16; b = -150; c = -300;
Δ = b2-4ac
Δ = -1502-4·16·(-300)
Δ = 41700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{41700}=\sqrt{100*417}=\sqrt{100}*\sqrt{417}=10\sqrt{417}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-10\sqrt{417}}{2*16}=\frac{150-10\sqrt{417}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+10\sqrt{417}}{2*16}=\frac{150+10\sqrt{417}}{32}
$