x+18/8=1x/4x

Solution for x+18/8=1x/4x equation:

x+18/8=1x/4x

We move all terms to the left:

x+18/8-(1x/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+1x/4x)+18/8=0

We get rid of parentheses

x-1x/4x+18/8=0

We calculate fractions


x+(-8x)/32x+72x/32x=0

We multiply all the terms by the denominator


x*32x+(-8x)+72x=0

We add all the numbers together, and all the variables

72x+x*32x+(-8x)=0

Wy multiply elements

32x^2+72x+(-8x)=0

We get rid of parentheses

32x^2+72x-8x=0

We add all the numbers together, and all the variables

32x^2+64x=0

a = 32; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·32·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*32}=\frac{-128}{64}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*32}=\frac{0}{64}
=0
$