Y=(5x+8)(4x+1)

Solution for Y=(5x+8)(4x+1) equation:

=(5Y+8)(4Y+1)

We move all terms to the left:

-((5Y+8)(4Y+1))=0

We multiply parentheses ..

-((+20Y^2+5Y+32Y+8))=0


We calculate terms in parentheses: -((+20Y^2+5Y+32Y+8)), so:

(+20Y^2+5Y+32Y+8)

We get rid of parentheses

20Y^2+5Y+32Y+8

We add all the numbers together, and all the variables

20Y^2+37Y+8

Back to the equation:

-(20Y^2+37Y+8)


We get rid of parentheses

-20Y^2-37Y-8=0

a = -20; b = -37; c = -8;
Δ = b2-4ac
Δ = -372-4·(-20)·(-8)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-27}{2*-20}=\frac{10}{-40}
=-1/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+27}{2*-20}=\frac{64}{-40}
=-1+3/5
$