6=-16t^2+112t+6

Solution for 6=-16t^2+112t+6 equation:

6=-16t^2+112t+6

We move all terms to the left:

6-(-16t^2+112t+6)=0

We get rid of parentheses

16t^2-112t-6+6=0

We add all the numbers together, and all the variables

16t^2-112t=0

a = 16; b = -112; c = 0;
Δ = b2-4ac
Δ = -1122-4·16·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-112}{2*16}=\frac{0}{32}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+112}{2*16}=\frac{224}{32}
=7
$