0=20+80t-(-5t^2)

Solution for 0=20+80t-(-5t^2) equation:

0=20+80t-(-5t^2)

We move all terms to the left:

0-(20+80t-(-5t^2))=0

We add all the numbers together, and all the variables

-(20+80t-(-5t^2))=0


We calculate terms in parentheses: -(20+80t-(-5t^2)), so:

20+80t-(-5t^2)

determiningTheFunctionDomain
-(-5t^2)+80t+20

We get rid of parentheses

5t^2+80t+20

Back to the equation:

-(5t^2+80t+20)


We get rid of parentheses

-5t^2-80t-20=0

a = -5; b = -80; c = -20;
Δ = b2-4ac
Δ = -802-4·(-5)·(-20)
Δ = 6000
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:

$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{15}}{2*-5}=\frac{80-20\sqrt{15}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{15}}{2*-5}=\frac{80+20\sqrt{15}}{-10}
$