Y=5x-0.15x^2+11

Solution for Y=5x-0.15x^2+11 equation:

=5Y-0.15Y^2+11

We move all terms to the left:

-(5Y-0.15Y^2+11)=0

We get rid of parentheses

0.15Y^2-5Y-11=0

a = 0.15; b = -5; c = -11;
Δ = b2-4ac
Δ = -52-4·0.15·(-11)
Δ = 31.6
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{-(-5)-\sqrt{31.6}}{2*0.15}=\frac{5-\sqrt{31.6}}{0.3}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{31.6}}{2*0.15}=\frac{5+\sqrt{31.6}}{0.3}
$