0=-16t^2+150t+400

Solution for 0=-16t^2+150t+400 equation:

0=-16t^2+150t+400

We move all terms to the left:

0-(-16t^2+150t+400)=0

We add all the numbers together, and all the variables

-(-16t^2+150t+400)=0

We get rid of parentheses

16t^2-150t-400=0

a = 16; b = -150; c = -400;
Δ = b2-4ac
Δ = -1502-4·16·(-400)
Δ = 48100
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:

$\sqrt{\Delta}=\sqrt{48100}=\sqrt{100*481}=\sqrt{100}*\sqrt{481}=10\sqrt{481}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-10\sqrt{481}}{2*16}=\frac{150-10\sqrt{481}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+10\sqrt{481}}{2*16}=\frac{150+10\sqrt{481}}{32}
$