0=(x+5)(x-1)

Solution for 0=(x+5)(x-1) equation:

0=(x+5)(x-1)

We move all terms to the left:

0-((x+5)(x-1))=0

We add all the numbers together, and all the variables

-((x+5)(x-1))=0

We multiply parentheses ..

-((+x^2-1x+5x-5))=0


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

(+x^2-1x+5x-5)

We get rid of parentheses

x^2-1x+5x-5

We add all the numbers together, and all the variables

x^2+4x-5

Back to the equation:

-(x^2+4x-5)


We get rid of parentheses

-x^2-4x+5=0

We add all the numbers together, and all the variables

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

a = -1; b = -4; c = +5;
Δ = b2-4ac
Δ = -42-4·(-1)·5
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*-1}=\frac{10}{-2}
=-5
$