-1/2x=2x-6

Solution for -1/2x=2x-6 equation:

-1/2x=2x-6

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x-2x+6=0

We multiply all the terms by the denominator


-2x*2x+6*2x-1=0

Wy multiply elements

-4x^2+12x-1=0

a = -4; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·(-4)·(-1)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{2}}{2*-4}=\frac{-12-8\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{2}}{2*-4}=\frac{-12+8\sqrt{2}}{-8}
$