6.5=-2.7x^2+40x+6.5

Solution for 6.5=-2.7x^2+40x+6.5 equation:

6.5=-2.7x^2+40x+6.5

We move all terms to the left:

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

We get rid of parentheses

2.7x^2-40x-6.5+6.5=0

We add all the numbers together, and all the variables

2.7x^2-40x=0

a = 2.7; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·2.7·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*2.7}=\frac{0}{5.4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*2.7}=\frac{80}{5.4}
=14+3.1428571428572/3.8571428571429
$