1/2x+5=5+2x

Solution for 1/2x+5=5+2x equation:

1/2x+5=5+2x

We move all terms to the left:

1/2x+5-(5+2x)=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-(2x+5)+5=0

We get rid of parentheses

1/2x-2x-5+5=0

We multiply all the terms by the denominator


-2x*2x-5*2x+5*2x+1=0

Wy multiply elements

-4x^2-10x+10x+1=0

We add all the numbers together, and all the variables

-4x^2+1=0

a = -4; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-4)·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*-4}=\frac{-4}{-8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*-4}=\frac{4}{-8}
=-1/2
$