5(t)=-16t^2+75t+80

Solution for 5(t)=-16t^2+75t+80 equation:

5(t)=-16t^2+75t+80

We move all terms to the left:

5(t)-(-16t^2+75t+80)=0

We get rid of parentheses

16t^2-75t+5t-80=0

We add all the numbers together, and all the variables

16t^2-70t-80=0

a = 16; b = -70; c = -80;
Δ = b2-4ac
Δ = -702-4·16·(-80)
Δ = 10020
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:

$\sqrt{\Delta}=\sqrt{10020}=\sqrt{4*2505}=\sqrt{4}*\sqrt{2505}=2\sqrt{2505}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{2505}}{2*16}=\frac{70-2\sqrt{2505}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{2505}}{2*16}=\frac{70+2\sqrt{2505}}{32}
$