0=(-16t^2)+400t+2400

Solution for 0=(-16t^2)+400t+2400 equation:

0=(-16t^2)+400t+2400

We move all terms to the left:

0-((-16t^2)+400t+2400)=0

We add all the numbers together, and all the variables

-((-16t^2)+400t+2400)=0


We calculate terms in parentheses: -((-16t^2)+400t+2400), so:

(-16t^2)+400t+2400

We get rid of parentheses

-16t^2+400t+2400

Back to the equation:

-(-16t^2+400t+2400)


We get rid of parentheses

16t^2-400t-2400=0

a = 16; b = -400; c = -2400;
Δ = b2-4ac
Δ = -4002-4·16·(-2400)
Δ = 313600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{313600}=560$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-560}{2*16}=\frac{-160}{32}
=-5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+560}{2*16}=\frac{960}{32}
=30
$