-4(x-8)=x(3x+4)

Solution for -4(x-8)=x(3x+4) equation:

-4(x-8)=x(3x+4)

We move all terms to the left:

-4(x-8)-(x(3x+4))=0

We multiply parentheses

-4x-(x(3x+4))+32=0


We calculate terms in parentheses: -(x(3x+4)), so:

x(3x+4)

We multiply parentheses

3x^2+4x

Back to the equation:

-(3x^2+4x)


We get rid of parentheses

-3x^2-4x-4x+32=0

We add all the numbers together, and all the variables

-3x^2-8x+32=0

a = -3; b = -8; c = +32;
Δ = b2-4ac
Δ = -82-4·(-3)·32
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{7}}{2*-3}=\frac{8-8\sqrt{7}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{7}}{2*-3}=\frac{8+8\sqrt{7}}{-6}
$