1/2x+87x=x+18

Solution for 1/2x+87x=x+18 equation:

1/2x+87x=x+18

We move all terms to the left:

1/2x+87x-(x+18)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

87x+1/2x-(x+18)=0

We get rid of parentheses

87x+1/2x-x-18=0

We multiply all the terms by the denominator


87x*2x-x*2x-18*2x+1=0

Wy multiply elements

174x^2-2x^2-36x+1=0

We add all the numbers together, and all the variables

172x^2-36x+1=0

a = 172; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·172·1
Δ = 608
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:

$\sqrt{\Delta}=\sqrt{608}=\sqrt{16*38}=\sqrt{16}*\sqrt{38}=4\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{38}}{2*172}=\frac{36-4\sqrt{38}}{344}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{38}}{2*172}=\frac{36+4\sqrt{38}}{344}
$