6=-16t^2+12t+40

Solution for 6=-16t^2+12t+40 equation:

6=-16t^2+12t+40

We move all terms to the left:

6-(-16t^2+12t+40)=0

We get rid of parentheses

16t^2-12t-40+6=0

We add all the numbers together, and all the variables

16t^2-12t-34=0

a = 16; b = -12; c = -34;
Δ = b2-4ac
Δ = -122-4·16·(-34)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{145}}{2*16}=\frac{12-4\sqrt{145}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{145}}{2*16}=\frac{12+4\sqrt{145}}{32}
$