-16t^2-40t+700=0

Solution for -16t^2-40t+700=0 equation:

-16t^2-40t+700=0

a = -16; b = -40; c = +700;
Δ = b2-4ac
Δ = -402-4·(-16)·700
Δ = 46400
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:

$\sqrt{\Delta}=\sqrt{46400}=\sqrt{1600*29}=\sqrt{1600}*\sqrt{29}=40\sqrt{29}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40\sqrt{29}}{2*-16}=\frac{40-40\sqrt{29}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40\sqrt{29}}{2*-16}=\frac{40+40\sqrt{29}}{-32}
$