0=-16t^2+186t+9

Solution for 0=-16t^2+186t+9 equation:

0=-16t^2+186t+9

We move all terms to the left:

0-(-16t^2+186t+9)=0

We add all the numbers together, and all the variables

-(-16t^2+186t+9)=0

We get rid of parentheses

16t^2-186t-9=0

a = 16; b = -186; c = -9;
Δ = b2-4ac
Δ = -1862-4·16·(-9)
Δ = 35172
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:

$\sqrt{\Delta}=\sqrt{35172}=\sqrt{36*977}=\sqrt{36}*\sqrt{977}=6\sqrt{977}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-186)-6\sqrt{977}}{2*16}=\frac{186-6\sqrt{977}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-186)+6\sqrt{977}}{2*16}=\frac{186+6\sqrt{977}}{32}
$