0=2.7t^2+40t+6.5

Solution for 0=2.7t^2+40t+6.5 equation:

0=2.7t^2+40t+6.5

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -2.7; b = -40; c = -6.5;
Δ = b2-4ac
Δ = -402-4·(-2.7)·(-6.5)
Δ = 1529.8
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{1529.8}}{2*-2.7}=\frac{40-\sqrt{1529.8}}{-5.4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+\sqrt{1529.8}}{2*-2.7}=\frac{40+\sqrt{1529.8}}{-5.4}
$