9+6t-t^2=t

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

9+6t-t^2=t

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1t^2+5t+9=0

a = -1; b = 5; c = +9;
Δ = b2-4ac
Δ = 52-4·(-1)·9
Δ = 61
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{-(5)-\sqrt{61}}{2*-1}=\frac{-5-\sqrt{61}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{61}}{2*-1}=\frac{-5+\sqrt{61}}{-2}
$