Y=(9x+1)(x-1)

Solution for Y=(9x+1)(x-1) equation:

=(9Y+1)(Y-1)

We move all terms to the left:

-((9Y+1)(Y-1))=0

We multiply parentheses ..

-((+9Y^2-9Y+Y-1))=0


We calculate terms in parentheses: -((+9Y^2-9Y+Y-1)), so:

(+9Y^2-9Y+Y-1)

We get rid of parentheses

9Y^2-9Y+Y-1

We add all the numbers together, and all the variables

9Y^2-8Y-1

Back to the equation:

-(9Y^2-8Y-1)


We get rid of parentheses

-9Y^2+8Y+1=0

a = -9; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-9)·1
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*-9}=\frac{-18}{-18}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*-9}=\frac{2}{-18}
=-1/9
$