1/2x-2x=3-5x

Solution for 1/2x-2x=3-5x equation:

1/2x-2x=3-5x

We move all terms to the left:

1/2x-2x-(3-5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-2x-(-5x+3)=0

We add all the numbers together, and all the variables

-2x+1/2x-(-5x+3)=0

We get rid of parentheses

-2x+1/2x+5x-3=0

We multiply all the terms by the denominator


-2x*2x+5x*2x-3*2x+1=0

Wy multiply elements

-4x^2+10x^2-6x+1=0

We add all the numbers together, and all the variables

6x^2-6x+1=0

a = 6; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·6·1
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*6}=\frac{6-2\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*6}=\frac{6+2\sqrt{3}}{12}
$