10=-2.7t^2+40t+6.5

Solution for 10=-2.7t^2+40t+6.5 equation:

10=-2.7t^2+40t+6.5

We move all terms to the left:

10-(-2.7t^2+40t+6.5)=0

We get rid of parentheses

2.7t^2-40t-6.5+10=0

We add all the numbers together, and all the variables

2.7t^2-40t+3.5=0

a = 2.7; b = -40; c = +3.5;
Δ = b2-4ac
Δ = -402-4·2.7·3.5
Δ = 1562.2
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{-(-40)-\sqrt{1562.2}}{2*2.7}=\frac{40-\sqrt{1562.2}}{5.4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+\sqrt{1562.2}}{2*2.7}=\frac{40+\sqrt{1562.2}}{5.4}
$