9=-16t^2+50t+6

Solution for 9=-16t^2+50t+6 equation:

9=-16t^2+50t+6

We move all terms to the left:

9-(-16t^2+50t+6)=0

We get rid of parentheses

16t^2-50t-6+9=0

We add all the numbers together, and all the variables

16t^2-50t+3=0

a = 16; b = -50; c = +3;
Δ = b2-4ac
Δ = -502-4·16·3
Δ = 2308
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:

$\sqrt{\Delta}=\sqrt{2308}=\sqrt{4*577}=\sqrt{4}*\sqrt{577}=2\sqrt{577}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{577}}{2*16}=\frac{50-2\sqrt{577}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{577}}{2*16}=\frac{50+2\sqrt{577}}{32}
$