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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -(-4(+Y^2+5Y-1Y-5)), so:

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

We multiply parentheses

-4Y^2-20Y+4Y+20

We add all the numbers together, and all the variables

-4Y^2-16Y+20

Back to the equation:

-(-4Y^2-16Y+20)


We get rid of parentheses

4Y^2+16Y-20=0

a = 4; b = 16; c = -20;
Δ = b2-4ac
Δ = 162-4·4·(-20)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-24}{2*4}=\frac{-40}{8}
=-5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+24}{2*4}=\frac{8}{8}
=1
$