0=(x+7)(x-13)

Solution for 0=(x+7)(x-13) equation:

0=(x+7)(x-13)

We move all terms to the left:

0-((x+7)(x-13))=0

We add all the numbers together, and all the variables

-((x+7)(x-13))=0

We multiply parentheses ..

-((+x^2-13x+7x-91))=0


We calculate terms in parentheses: -((+x^2-13x+7x-91)), so:

(+x^2-13x+7x-91)

We get rid of parentheses

x^2-13x+7x-91

We add all the numbers together, and all the variables

x^2-6x-91

Back to the equation:

-(x^2-6x-91)


We get rid of parentheses

-x^2+6x+91=0

We add all the numbers together, and all the variables

-1x^2+6x+91=0

a = -1; b = 6; c = +91;
Δ = b2-4ac
Δ = 62-4·(-1)·91
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-20}{2*-1}=\frac{-26}{-2}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+20}{2*-1}=\frac{14}{-2}
=-7
$