-2.71x^2+40x+6.5=12

Solution for -2.71x^2+40x+6.5=12 equation:

-2.71x^2+40x+6.5=12

We move all terms to the left:

-2.71x^2+40x+6.5-(12)=0

We add all the numbers together, and all the variables

-2.71x^2+40x-5.5=0

a = -2.71; b = 40; c = -5.5;
Δ = b2-4ac
Δ = 402-4·(-2.71)·(-5.5)
Δ = 1540.38
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-\sqrt{1540.38}}{2*-2.71}=\frac{-40-\sqrt{1540.38}}{-5.42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+\sqrt{1540.38}}{2*-2.71}=\frac{-40+\sqrt{1540.38}}{-5.42}
$