10=112t-16t^2

Solution for 10=112t-16t^2 equation:

10=112t-16t^2

We move all terms to the left:

10-(112t-16t^2)=0

We get rid of parentheses

16t^2-112t+10=0

a = 16; b = -112; c = +10;
Δ = b2-4ac
Δ = -1122-4·16·10
Δ = 11904
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:

$\sqrt{\Delta}=\sqrt{11904}=\sqrt{64*186}=\sqrt{64}*\sqrt{186}=8\sqrt{186}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-8\sqrt{186}}{2*16}=\frac{112-8\sqrt{186}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+8\sqrt{186}}{2*16}=\frac{112+8\sqrt{186}}{32}
$