4x(x-8)=-2(3x-6)

Solution for 4x(x-8)=-2(3x-6) equation:

4x(x-8)=-2(3x-6)

We move all terms to the left:

4x(x-8)-(-2(3x-6))=0

We multiply parentheses

4x^2-32x-(-2(3x-6))=0


We calculate terms in parentheses: -(-2(3x-6)), so:

-2(3x-6)

We multiply parentheses

-6x+12

Back to the equation:

-(-6x+12)


We get rid of parentheses

4x^2-32x+6x-12=0

We add all the numbers together, and all the variables

4x^2-26x-12=0

a = 4; b = -26; c = -12;
Δ = b2-4ac
Δ = -262-4·4·(-12)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{217}}{2*4}=\frac{26-2\sqrt{217}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{217}}{2*4}=\frac{26+2\sqrt{217}}{8}
$