32x-8=(14x+4)(4x-8)

Solution for 32x-8=(14x+4)(4x-8) equation:

32x-8=(14x+4)(4x-8)

We move all terms to the left:

32x-8-((14x+4)(4x-8))=0

We multiply parentheses ..

-((+56x^2-112x+16x-32))+32x-8=0


We calculate terms in parentheses: -((+56x^2-112x+16x-32)), so:

(+56x^2-112x+16x-32)

We get rid of parentheses

56x^2-112x+16x-32

We add all the numbers together, and all the variables

56x^2-96x-32

Back to the equation:

-(56x^2-96x-32)


We add all the numbers together, and all the variables

32x-(56x^2-96x-32)-8=0

We get rid of parentheses

-56x^2+32x+96x+32-8=0

We add all the numbers together, and all the variables

-56x^2+128x+24=0

a = -56; b = 128; c = +24;
Δ = b2-4ac
Δ = 1282-4·(-56)·24
Δ = 21760
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:

$\sqrt{\Delta}=\sqrt{21760}=\sqrt{256*85}=\sqrt{256}*\sqrt{85}=16\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-16\sqrt{85}}{2*-56}=\frac{-128-16\sqrt{85}}{-112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+16\sqrt{85}}{2*-56}=\frac{-128+16\sqrt{85}}{-112}
$