Y=5x-9(x)2

Solution for Y=5x-9(x)2 equation:

=5Y-9(Y)2

We move all terms to the left:

-(5Y-9(Y)2)=0

We add all the numbers together, and all the variables

-(+5Y-9Y^2)=0

We get rid of parentheses

9Y^2-5Y=0

a = 9; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·9·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*9}=\frac{0}{18}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*9}=\frac{10}{18}
=5/9
$