-2.7t^2+30t+6.5=12

Solution for -2.7t^2+30t+6.5=12 equation:

-2.7t^2+30t+6.5=12

We move all terms to the left:

-2.7t^2+30t+6.5-(12)=0

We add all the numbers together, and all the variables

-2.7t^2+30t-5.5=0

a = -2.7; b = 30; c = -5.5;
Δ = b2-4ac
Δ = 302-4·(-2.7)·(-5.5)
Δ = 840.6
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{-(30)-\sqrt{840.6}}{2*-2.7}=\frac{-30-\sqrt{840.6}}{-5.4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+\sqrt{840.6}}{2*-2.7}=\frac{-30+\sqrt{840.6}}{-5.4}
$