7x-4(x-8)=-8x(8-6x)

Solution for 7x-4(x-8)=-8x(8-6x) equation:

7x-4(x-8)=-8x(8-6x)

We move all terms to the left:

7x-4(x-8)-(-8x(8-6x))=0

We add all the numbers together, and all the variables

7x-4(x-8)-(-8x(-6x+8))=0

We multiply parentheses

7x-4x-(-8x(-6x+8))+32=0


We calculate terms in parentheses: -(-8x(-6x+8)), so:

-8x(-6x+8)

We multiply parentheses

48x^2-64x

Back to the equation:

-(48x^2-64x)


We add all the numbers together, and all the variables

3x-(48x^2-64x)+32=0

We get rid of parentheses

-48x^2+3x+64x+32=0

We add all the numbers together, and all the variables

-48x^2+67x+32=0

a = -48; b = 67; c = +32;
Δ = b2-4ac
Δ = 672-4·(-48)·32
Δ = 10633
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:

$\sqrt{\Delta}=\sqrt{10633}=\sqrt{49*217}=\sqrt{49}*\sqrt{217}=7\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(67)-7\sqrt{217}}{2*-48}=\frac{-67-7\sqrt{217}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+7\sqrt{217}}{2*-48}=\frac{-67+7\sqrt{217}}{-96}
$