4x(x-1)=2(6-2x)

Solution for 4x(x-1)=2(6-2x) equation:

4x(x-1)=2(6-2x)

We move all terms to the left:

4x(x-1)-(2(6-2x))=0

We add all the numbers together, and all the variables

4x(x-1)-(2(-2x+6))=0

We multiply parentheses

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


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

2(-2x+6)

We multiply parentheses

-4x+12

Back to the equation:

-(-4x+12)


We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-12=0

a = 4; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·4·(-12)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*4}=\frac{0-8\sqrt{3}}{8}
=-\frac{8\sqrt{3}}{8}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*4}=\frac{0+8\sqrt{3}}{8}
=\frac{8\sqrt{3}}{8}
=\sqrt{3}
$