(t)=16t^2+79t+5

Solution for (t)=16t^2+79t+5 equation:

(t)=16t^2+79t+5

We move all terms to the left:

(t)-(16t^2+79t+5)=0

We get rid of parentheses

-16t^2+t-79t-5=0

We add all the numbers together, and all the variables

-16t^2-78t-5=0

a = -16; b = -78; c = -5;
Δ = b2-4ac
Δ = -782-4·(-16)·(-5)
Δ = 5764
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:

$\sqrt{\Delta}=\sqrt{5764}=\sqrt{4*1441}=\sqrt{4}*\sqrt{1441}=2\sqrt{1441}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1441}}{2*-16}=\frac{78-2\sqrt{1441}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1441}}{2*-16}=\frac{78+2\sqrt{1441}}{-32}
$