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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+5Y^2-5Y+4Y-4))=0


We calculate terms in parentheses: -((+5Y^2-5Y+4Y-4)), so:

(+5Y^2-5Y+4Y-4)

We get rid of parentheses

5Y^2-5Y+4Y-4

We add all the numbers together, and all the variables

5Y^2-1Y-4

Back to the equation:

-(5Y^2-1Y-4)


We get rid of parentheses

-5Y^2+1Y+4=0

We add all the numbers together, and all the variables

-5Y^2+Y+4=0

a = -5; b = 1; c = +4;
Δ = b2-4ac
Δ = 12-4·(-5)·4
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*-5}=\frac{-10}{-10}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*-5}=\frac{8}{-10}
=-4/5
$