1/2x-2x=4x-23

Solution for 1/2x-2x=4x-23 equation:

1/2x-2x=4x-23

We move all terms to the left:

1/2x-2x-(4x-23)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+1/2x-(4x-23)=0

We get rid of parentheses

-2x+1/2x-4x+23=0

We multiply all the terms by the denominator


-2x*2x-4x*2x+23*2x+1=0

Wy multiply elements

-4x^2-8x^2+46x+1=0

We add all the numbers together, and all the variables

-12x^2+46x+1=0

a = -12; b = 46; c = +1;
Δ = b2-4ac
Δ = 462-4·(-12)·1
Δ = 2164
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:

$\sqrt{\Delta}=\sqrt{2164}=\sqrt{4*541}=\sqrt{4}*\sqrt{541}=2\sqrt{541}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{541}}{2*-12}=\frac{-46-2\sqrt{541}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{541}}{2*-12}=\frac{-46+2\sqrt{541}}{-24}
$