-4+x=1/2x-2

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

-4+x=1/2x-2

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

2x^2-4x-1=0

a = 2; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·2·(-1)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{6}}{2*2}=\frac{4-2\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{6}}{2*2}=\frac{4+2\sqrt{6}}{4}
$