Y=-0.15x^2+2.7x+6

Solution for Y=-0.15x^2+2.7x+6 equation:

=-0.15Y^2+2.7Y+6

We move all terms to the left:

-(-0.15Y^2+2.7Y+6)=0

We get rid of parentheses

0.15Y^2-2.7Y-6=0

a = 0.15; b = -2.7; c = -6;
Δ = b2-4ac
Δ = -2.72-4·0.15·(-6)
Δ = 10.89
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{-(-2.7)-\sqrt{10.89}}{2*0.15}=\frac{2.7-\sqrt{10.89}}{0.3}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.7)+\sqrt{10.89}}{2*0.15}=\frac{2.7+\sqrt{10.89}}{0.3}
$