0=-16t^2+89t+4

Solution for 0=-16t^2+89t+4 equation:

0=-16t^2+89t+4

We move all terms to the left:

0-(-16t^2+89t+4)=0

We add all the numbers together, and all the variables

-(-16t^2+89t+4)=0

We get rid of parentheses

16t^2-89t-4=0

a = 16; b = -89; c = -4;
Δ = b2-4ac
Δ = -892-4·16·(-4)
Δ = 8177
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{-(-89)-\sqrt{8177}}{2*16}=\frac{89-\sqrt{8177}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+\sqrt{8177}}{2*16}=\frac{89+\sqrt{8177}}{32}
$