Y=x(9x-5)

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

=Y(9Y-5)

We move all terms to the left:

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


We calculate terms in parentheses: -(Y(9Y-5)), so:

Y(9Y-5)

We multiply parentheses

9Y^2-5Y

Back to the equation:

-(9Y^2-5Y)


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