0=-16t^2+80t+150

Solution for 0=-16t^2+80t+150 equation:

0=-16t^2+80t+150

We move all terms to the left:

0-(-16t^2+80t+150)=0

We add all the numbers together, and all the variables

-(-16t^2+80t+150)=0

We get rid of parentheses

16t^2-80t-150=0

a = 16; b = -80; c = -150;
Δ = b2-4ac
Δ = -802-4·16·(-150)
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-40\sqrt{10}}{2*16}=\frac{80-40\sqrt{10}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+40\sqrt{10}}{2*16}=\frac{80+40\sqrt{10}}{32}
$