0=16t^2-40t+10

Solution for 0=16t^2-40t+10 equation:

0=16t^2-40t+10

We move all terms to the left:

0-(16t^2-40t+10)=0

We add all the numbers together, and all the variables

-(16t^2-40t+10)=0

We get rid of parentheses

-16t^2+40t-10=0

a = -16; b = 40; c = -10;
Δ = b2-4ac
Δ = 402-4·(-16)·(-10)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{15}}{2*-16}=\frac{-40-8\sqrt{15}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{15}}{2*-16}=\frac{-40+8\sqrt{15}}{-32}
$