Y=(9x+8)(5x-9)

Solution for Y=(9x+8)(5x-9) equation:

=(9Y+8)(5Y-9)

We move all terms to the left:

-((9Y+8)(5Y-9))=0

We multiply parentheses ..

-((+45Y^2-81Y+40Y-72))=0


We calculate terms in parentheses: -((+45Y^2-81Y+40Y-72)), so:

(+45Y^2-81Y+40Y-72)

We get rid of parentheses

45Y^2-81Y+40Y-72

We add all the numbers together, and all the variables

45Y^2-41Y-72

Back to the equation:

-(45Y^2-41Y-72)


We get rid of parentheses

-45Y^2+41Y+72=0

a = -45; b = 41; c = +72;
Δ = b2-4ac
Δ = 412-4·(-45)·72
Δ = 14641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14641}=121$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-121}{2*-45}=\frac{-162}{-90}
=1+4/5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+121}{2*-45}=\frac{80}{-90}
=-8/9
$