0=2.7t^2-40t-11.5

Solution for 0=2.7t^2-40t-11.5 equation:

0=2.7t^2-40t-11.5

We move all terms to the left:

0-(2.7t^2-40t-11.5)=0

We add all the numbers together, and all the variables

-(2.7t^2-40t-11.5)=0

We get rid of parentheses

-2.7t^2+40t+11.5=0

a = -2.7; b = 40; c = +11.5;
Δ = b2-4ac
Δ = 402-4·(-2.7)·11.5
Δ = 1724.2
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{1724.2}}{2*-2.7}=\frac{-40-\sqrt{1724.2}}{-5.4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+\sqrt{1724.2}}{2*-2.7}=\frac{-40+\sqrt{1724.2}}{-5.4}
$