t=-16t^2+155t+76

Solution for t=-16t^2+155t+76 equation:

t=-16t^2+155t+76

We move all terms to the left:

t-(-16t^2+155t+76)=0

We get rid of parentheses

16t^2-155t+t-76=0

We add all the numbers together, and all the variables

16t^2-154t-76=0

a = 16; b = -154; c = -76;
Δ = b2-4ac
Δ = -1542-4·16·(-76)
Δ = 28580
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:

$\sqrt{\Delta}=\sqrt{28580}=\sqrt{4*7145}=\sqrt{4}*\sqrt{7145}=2\sqrt{7145}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-154)-2\sqrt{7145}}{2*16}=\frac{154-2\sqrt{7145}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-154)+2\sqrt{7145}}{2*16}=\frac{154+2\sqrt{7145}}{32}
$