1/2x+4=-x-2

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

1/2x+4=-x-2

We move all terms to the left:

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

We get rid of parentheses

1/2x+1x+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+12x+1=0

a = 2; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·2·1
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{34}}{2*2}=\frac{-12-2\sqrt{34}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{34}}{2*2}=\frac{-12+2\sqrt{34}}{4}
$