1/2x+1/2x=x+4

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

1/2x+1/2x=x+4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -2; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·(-2)·2
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{5}}{2*-2}=\frac{8-4\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{5}}{2*-2}=\frac{8+4\sqrt{5}}{-4}
$