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

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

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

We move all terms to the left:

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


Domain of the equation: 2x-6))!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

4x*2x-6*2x-6))-(2(-5))=0

We add all the numbers together, and all the variables

4x*2x-6*2x=0

Wy multiply elements

8x^2-12x=0

a = 8; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·8·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*8}=\frac{24}{16}
=1+1/2
$