0=(x-8)(x+7)

Solution for 0=(x-8)(x+7) equation:

0=(x-8)(x+7)

We move all terms to the left:

0-((x-8)(x+7))=0

We add all the numbers together, and all the variables

-((x-8)(x+7))=0

We multiply parentheses ..

-((+x^2+7x-8x-56))=0


We calculate terms in parentheses: -((+x^2+7x-8x-56)), so:

(+x^2+7x-8x-56)

We get rid of parentheses

x^2+7x-8x-56

We add all the numbers together, and all the variables

x^2-1x-56

Back to the equation:

-(x^2-1x-56)


We get rid of parentheses

-x^2+1x+56=0

We add all the numbers together, and all the variables

-1x^2+x+56=0

a = -1; b = 1; c = +56;
Δ = b2-4ac
Δ = 12-4·(-1)·56
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*-1}=\frac{14}{-2}
=-7
$