0=16+4t(t-6)

Solution for 0=16+4t(t-6) equation:

0=16+4t(t-6)

We move all terms to the left:

0-(16+4t(t-6))=0

We add all the numbers together, and all the variables

-(16+4t(t-6))=0


We calculate terms in parentheses: -(16+4t(t-6)), so:

16+4t(t-6)

determiningTheFunctionDomain
4t(t-6)+16

We multiply parentheses

4t^2-24t+16

Back to the equation:

-(4t^2-24t+16)


We get rid of parentheses

-4t^2+24t-16=0

a = -4; b = 24; c = -16;
Δ = b2-4ac
Δ = 242-4·(-4)·(-16)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{5}}{2*-4}=\frac{-24-8\sqrt{5}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{5}}{2*-4}=\frac{-24+8\sqrt{5}}{-8}
$