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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-1x*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}
$