(-2t-5)(8t-5)=0

Solution for (-2t-5)(8t-5)=0 equation:

(-2t-5)(8t-5)=0

We multiply parentheses ..

(-16t^2+10t-40t+25)=0

We get rid of parentheses

-16t^2+10t-40t+25=0

We add all the numbers together, and all the variables

-16t^2-30t+25=0

a = -16; b = -30; c = +25;
Δ = b2-4ac
Δ = -302-4·(-16)·25
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-50}{2*-16}=\frac{-20}{-32}
=5/8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+50}{2*-16}=\frac{80}{-32}
=-2+1/2
$