5+18-x=4+1/3x

Solution for 5+18-x=4+1/3x equation:

5+18-x=4+1/3x

We move all terms to the left:

5+18-x-(4+1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(1/3x+4)+5+18=0

We add all the numbers together, and all the variables

-1x-(1/3x+4)+23=0

We get rid of parentheses

-1x-1/3x-4+23=0

We multiply all the terms by the denominator


-1x*3x-4*3x+23*3x-1=0

Wy multiply elements

-3x^2-12x+69x-1=0

We add all the numbers together, and all the variables

-3x^2+57x-1=0

a = -3; b = 57; c = -1;
Δ = b2-4ac
Δ = 572-4·(-3)·(-1)
Δ = 3237
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-\sqrt{3237}}{2*-3}=\frac{-57-\sqrt{3237}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+\sqrt{3237}}{2*-3}=\frac{-57+\sqrt{3237}}{-6}
$