-4(4t^2-21t-25)=0

Solution for -4(4t^2-21t-25)=0 equation:

-4(4t^2-21t-25)=0

We multiply parentheses

-16t^2+84t+100=0

a = -16; b = 84; c = +100;
Δ = b2-4ac
Δ = 842-4·(-16)·100
Δ = 13456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13456}=116$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-116}{2*-16}=\frac{-200}{-32}
=6+1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+116}{2*-16}=\frac{32}{-32}
=-1
$