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

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

=-2.7Y^2+40Y+6.5

We move all terms to the left:

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

We get rid of parentheses

2.7Y^2-40Y-6.5=0

a = 2.7; b = -40; c = -6.5;
Δ = b2-4ac
Δ = -402-4·2.7·(-6.5)
Δ = 1670.2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-\sqrt{1670.2}}{2*2.7}=\frac{40-\sqrt{1670.2}}{5.4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+\sqrt{1670.2}}{2*2.7}=\frac{40+\sqrt{1670.2}}{5.4}
$