0=-16t^2+40t+906

Solution for 0=-16t^2+40t+906 equation:

0=-16t^2+40t+906

We move all terms to the left:

0-(-16t^2+40t+906)=0

We add all the numbers together, and all the variables

-(-16t^2+40t+906)=0

We get rid of parentheses

16t^2-40t-906=0

a = 16; b = -40; c = -906;
Δ = b2-4ac
Δ = -402-4·16·(-906)
Δ = 59584
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:

$\sqrt{\Delta}=\sqrt{59584}=\sqrt{3136*19}=\sqrt{3136}*\sqrt{19}=56\sqrt{19}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-56\sqrt{19}}{2*16}=\frac{40-56\sqrt{19}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+56\sqrt{19}}{2*16}=\frac{40+56\sqrt{19}}{32}
$