10=-16t^2+32t+6

Solution for 10=-16t^2+32t+6 equation:

10=-16t^2+32t+6

We move all terms to the left:

10-(-16t^2+32t+6)=0

We get rid of parentheses

16t^2-32t-6+10=0

We add all the numbers together, and all the variables

16t^2-32t+4=0

a = 16; b = -32; c = +4;
Δ = b2-4ac
Δ = -322-4·16·4
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-16\sqrt{3}}{2*16}=\frac{32-16\sqrt{3}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+16\sqrt{3}}{2*16}=\frac{32+16\sqrt{3}}{32}
$