4(x-6)=16x+4(x^2-4)

Solution for 4(x-6)=16x+4(x^2-4) equation:

4(x-6)=16x+4(x^2-4)

We move all terms to the left:

4(x-6)-(16x+4(x^2-4))=0

We multiply parentheses

4x-(16x+4(x^2-4))-24=0


We calculate terms in parentheses: -(16x+4(x^2-4)), so:

16x+4(x^2-4)

We multiply parentheses

4x^2+16x-16

Back to the equation:

-(4x^2+16x-16)


We get rid of parentheses

-4x^2+4x-16x+16-24=0

We add all the numbers together, and all the variables

-4x^2-12x-8=0

a = -4; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·(-4)·(-8)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4}{2*-4}=\frac{8}{-8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4}{2*-4}=\frac{16}{-8}
=-2
$