(-2t+8)(8t-2)=0

Solution for (-2t+8)(8t-2)=0 equation:

(-2t+8)(8t-2)=0

We multiply parentheses ..

(-16t^2+4t+64t-16)=0

We get rid of parentheses

-16t^2+4t+64t-16=0

We add all the numbers together, and all the variables

-16t^2+68t-16=0

a = -16; b = 68; c = -16;
Δ = b2-4ac
Δ = 682-4·(-16)·(-16)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-60}{2*-16}=\frac{-128}{-32}
=+4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+60}{2*-16}=\frac{-8}{-32}
=1/4
$