20=-2.71x^2+40x+6.5

Solution for 20=-2.71x^2+40x+6.5 equation:

20=-2.71x^2+40x+6.5

We move all terms to the left:

20-(-2.71x^2+40x+6.5)=0

We get rid of parentheses

2.71x^2-40x-6.5+20=0

We add all the numbers together, and all the variables

2.71x^2-40x+13.5=0

a = 2.71; b = -40; c = +13.5;
Δ = b2-4ac
Δ = -402-4·2.71·13.5
Δ = 1453.66
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{1453.66}}{2*2.71}=\frac{40-\sqrt{1453.66}}{5.42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+\sqrt{1453.66}}{2*2.71}=\frac{40+\sqrt{1453.66}}{5.42}
$