100(t)=112+96t-16t^2

Solution for 100(t)=112+96t-16t^2 equation:

100(t)=112+96t-16t^2

We move all terms to the left:

100(t)-(112+96t-16t^2)=0

We get rid of parentheses

16t^2-96t+100t-112=0

We add all the numbers together, and all the variables

16t^2+4t-112=0

a = 16; b = 4; c = -112;
Δ = b2-4ac
Δ = 42-4·16·(-112)
Δ = 7184
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:

$\sqrt{\Delta}=\sqrt{7184}=\sqrt{16*449}=\sqrt{16}*\sqrt{449}=4\sqrt{449}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{449}}{2*16}=\frac{-4-4\sqrt{449}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{449}}{2*16}=\frac{-4+4\sqrt{449}}{32}
$