9=-16t^2+100

Solution for 9=-16t^2+100 equation:

9=-16t^2+100

We move all terms to the left:

9-(-16t^2+100)=0

We get rid of parentheses

16t^2-100+9=0

We add all the numbers together, and all the variables

16t^2-91=0

a = 16; b = 0; c = -91;
Δ = b2-4ac
Δ = 02-4·16·(-91)
Δ = 5824
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:

$\sqrt{\Delta}=\sqrt{5824}=\sqrt{64*91}=\sqrt{64}*\sqrt{91}=8\sqrt{91}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{91}}{2*16}=\frac{0-8\sqrt{91}}{32}
=-\frac{8\sqrt{91}}{32}
=-\frac{\sqrt{91}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{91}}{2*16}=\frac{0+8\sqrt{91}}{32}
=\frac{8\sqrt{91}}{32}
=\frac{\sqrt{91}}{4}
$