9.088=36.8t-3.55t^2

Solution for 9.088=36.8t-3.55t^2 equation:

9.088=36.8t-3.55t^2

We move all terms to the left:

9.088-(36.8t-3.55t^2)=0

We get rid of parentheses

3.55t^2-36.8t+9.088=0

a = 3.55; b = -36.8; c = +9.088;
Δ = b2-4ac
Δ = -36.82-4·3.55·9.088
Δ = 1225.1904
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{-(-36.8)-\sqrt{1225.1904}}{2*3.55}=\frac{36.8-\sqrt{1225.1904}}{7.1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36.8)+\sqrt{1225.1904}}{2*3.55}=\frac{36.8+\sqrt{1225.1904}}{7.1}
$