784(t)=-16t^2+784

Solution for 784(t)=-16t^2+784 equation:

784(t)=-16t^2+784

We move all terms to the left:

784(t)-(-16t^2+784)=0

We get rid of parentheses

16t^2+784t-784=0

a = 16; b = 784; c = -784;
Δ = b2-4ac
Δ = 7842-4·16·(-784)
Δ = 664832
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:

$\sqrt{\Delta}=\sqrt{664832}=\sqrt{12544*53}=\sqrt{12544}*\sqrt{53}=112\sqrt{53}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(784)-112\sqrt{53}}{2*16}=\frac{-784-112\sqrt{53}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(784)+112\sqrt{53}}{2*16}=\frac{-784+112\sqrt{53}}{32}
$