-16t^2+42+5=0

Solution for -16t^2+42+5=0 equation:

-16t^2+42+5=0

We add all the numbers together, and all the variables

-16t^2+47=0

a = -16; b = 0; c = +47;
Δ = b2-4ac
Δ = 02-4·(-16)·47
Δ = 3008
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:

$\sqrt{\Delta}=\sqrt{3008}=\sqrt{64*47}=\sqrt{64}*\sqrt{47}=8\sqrt{47}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{47}}{2*-16}=\frac{0-8\sqrt{47}}{-32}
=-\frac{8\sqrt{47}}{-32}
=-\frac{\sqrt{47}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{47}}{2*-16}=\frac{0+8\sqrt{47}}{-32}
=\frac{8\sqrt{47}}{-32}
=\frac{\sqrt{47}}{-4}
$