5(t)=16t^2+64t+5

Solution for 5(t)=16t^2+64t+5 equation:

5(t)=16t^2+64t+5

We move all terms to the left:

5(t)-(16t^2+64t+5)=0

We get rid of parentheses

-16t^2+5t-64t-5=0

We add all the numbers together, and all the variables

-16t^2-59t-5=0

a = -16; b = -59; c = -5;
Δ = b2-4ac
Δ = -592-4·(-16)·(-5)
Δ = 3161
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{-(-59)-\sqrt{3161}}{2*-16}=\frac{59-\sqrt{3161}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{3161}}{2*-16}=\frac{59+\sqrt{3161}}{-32}
$