-16(t^2-10t-75)=0

Solution for -16(t^2-10t-75)=0 equation:

-16(t^2-10t-75)=0

We multiply parentheses

-16t^2+160t+1200=0

a = -16; b = 160; c = +1200;
Δ = b2-4ac
Δ = 1602-4·(-16)·1200
Δ = 102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400}=320$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-320}{2*-16}=\frac{-480}{-32}
=+15
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+320}{2*-16}=\frac{160}{-32}
=-5
$