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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+7x^2-49x+8x-56))=0


We calculate terms in parentheses: -((+7x^2-49x+8x-56)), so:

(+7x^2-49x+8x-56)

We get rid of parentheses

7x^2-49x+8x-56

We add all the numbers together, and all the variables

7x^2-41x-56

Back to the equation:

-(7x^2-41x-56)


We get rid of parentheses

-7x^2+41x+56=0

a = -7; b = 41; c = +56;
Δ = b2-4ac
Δ = 412-4·(-7)·56
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-57}{2*-7}=\frac{-98}{-14}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+57}{2*-7}=\frac{16}{-14}
=-1+1/7
$