10=32t-16t^2

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

10=32t-16t^2

We move all terms to the left:

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

We get rid of parentheses

16t^2-32t+10=0

a = 16; b = -32; c = +10;
Δ = b2-4ac
Δ = -322-4·16·10
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{6}}{2*16}=\frac{32-8\sqrt{6}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{6}}{2*16}=\frac{32+8\sqrt{6}}{32}
$