t=16t^2+112t+10

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

t=16t^2+112t+10

We move all terms to the left:

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

We get rid of parentheses

-16t^2+t-112t-10=0

We add all the numbers together, and all the variables

-16t^2-111t-10=0

a = -16; b = -111; c = -10;
Δ = b2-4ac
Δ = -1112-4·(-16)·(-10)
Δ = 11681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-111)-\sqrt{11681}}{2*-16}=\frac{111-\sqrt{11681}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111)+\sqrt{11681}}{2*-16}=\frac{111+\sqrt{11681}}{-32}
$