(7x-16)(x+8)=4x

Solution for (7x-16)(x+8)=4x equation:

(7x-16)(x+8)=4x

We move all terms to the left:

(7x-16)(x+8)-(4x)=0

We add all the numbers together, and all the variables

-4x+(7x-16)(x+8)=0

We multiply parentheses ..

(+7x^2+56x-16x-128)-4x=0

We get rid of parentheses

7x^2+56x-16x-4x-128=0

We add all the numbers together, and all the variables

7x^2+36x-128=0

a = 7; b = 36; c = -128;
Δ = b2-4ac
Δ = 362-4·7·(-128)
Δ = 4880
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4880}=\sqrt{16*305}=\sqrt{16}*\sqrt{305}=4\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{305}}{2*7}=\frac{-36-4\sqrt{305}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{305}}{2*7}=\frac{-36+4\sqrt{305}}{14}
$