9+6t-t^2=0

Solution for 9+6t-t^2=0 equation:

9+6t-t^2=0

We add all the numbers together, and all the variables

-1t^2+6t+9=0

a = -1; b = 6; c = +9;
Δ = b2-4ac
Δ = 62-4·(-1)·9
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{2}}{2*-1}=\frac{-6-6\sqrt{2}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{2}}{2*-1}=\frac{-6+6\sqrt{2}}{-2}
$