112t-16t^2=10

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

112t-16t^2=10

We move all terms to the left:

112t-16t^2-(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}
$