5.5=-2t^2+9t+11

Solution for 5.5=-2t^2+9t+11 equation:

5.5=-2t^2+9t+11

We move all terms to the left:

5.5-(-2t^2+9t+11)=0

We get rid of parentheses

2t^2-9t-11+5.5=0

We add all the numbers together, and all the variables

2t^2-9t-5.5=0

a = 2; b = -9; c = -5.5;
Δ = b2-4ac
Δ = -92-4·2·(-5.5)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5\sqrt{5}}{2*2}=\frac{9-5\sqrt{5}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5\sqrt{5}}{2*2}=\frac{9+5\sqrt{5}}{4}
$