-8t(2t-3)=0

Solution for -8t(2t-3)=0 equation:

-8t(2t-3)=0

We multiply parentheses

-16t^2+24t=0

a = -16; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-16)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-16}=\frac{-48}{-32}
=1+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-16}=\frac{0}{-32}
=0
$