(x-4)(x+7)=8x(x+7)

Solution for (x-4)(x+7)=8x(x+7) equation:

(x-4)(x+7)=8x(x+7)

We move all terms to the left:

(x-4)(x+7)-(8x(x+7))=0

We multiply parentheses ..

(+x^2+7x-4x-28)-(8x(x+7))=0


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

8x(x+7)

We multiply parentheses

8x^2+56x

Back to the equation:

-(8x^2+56x)


We get rid of parentheses

x^2-8x^2+7x-4x-56x-28=0

We add all the numbers together, and all the variables

-7x^2-53x-28=0

a = -7; b = -53; c = -28;
Δ = b2-4ac
Δ = -532-4·(-7)·(-28)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-45}{2*-7}=\frac{8}{-14}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+45}{2*-7}=\frac{98}{-14}
=-7
$