1/2x+4=13/18x

Solution for 1/2x+4=13/18x equation:

1/2x+4=13/18x

We move all terms to the left:

1/2x+4-(13/18x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 18x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+13/18x)+4=0

We get rid of parentheses

1/2x-13/18x+4=0

We calculate fractions


18x/36x^2+(-26x)/36x^2+4=0

We multiply all the terms by the denominator


18x+(-26x)+4*36x^2=0

Wy multiply elements

144x^2+18x+(-26x)=0

We get rid of parentheses

144x^2+18x-26x=0

We add all the numbers together, and all the variables

144x^2-8x=0

a = 144; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·144·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*144}=\frac{0}{288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*144}=\frac{16}{288}
=1/18
$