-16t^2-21+106=0

Solution for -16t^2-21+106=0 equation:

-16t^2-21+106=0

We add all the numbers together, and all the variables

-16t^2+85=0

a = -16; b = 0; c = +85;
Δ = b2-4ac
Δ = 02-4·(-16)·85
Δ = 5440
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5440}=\sqrt{64*85}=\sqrt{64}*\sqrt{85}=8\sqrt{85}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{85}}{2*-16}=\frac{0-8\sqrt{85}}{-32}
=-\frac{8\sqrt{85}}{-32}
=-\frac{\sqrt{85}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{85}}{2*-16}=\frac{0+8\sqrt{85}}{-32}
=\frac{8\sqrt{85}}{-32}
=\frac{\sqrt{85}}{-4}
$