x=2(3x-1)-4x+1/2

Solution for x=2(3x-1)-4x+1/2 equation:

x=2(3x-1)-4x+1/2

We move all terms to the left:

x-(2(3x-1)-4x+1/2)=0

We multiply all the terms by the denominator


x*2)-(2(3x-1)-4x+1=0

We add all the numbers together, and all the variables

-4x+x*2)-(2(3x-1)+1=0

Wy multiply elements

2x^2-4x+1=0

a = 2; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·2·1
Δ = 8
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:

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