18+2/3x+4=2x-5-x

Solution for 18+2/3x+4=2x-5-x equation:

18+2/3x+4=2x-5-x

We move all terms to the left:

18+2/3x+4-(2x-5-x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(x-5)+18+4=0

We add all the numbers together, and all the variables

2/3x-(x-5)+22=0

We get rid of parentheses

2/3x-x+5+22=0

We multiply all the terms by the denominator


-x*3x+5*3x+22*3x+2=0

Wy multiply elements

-3x^2+15x+66x+2=0

We add all the numbers together, and all the variables

-3x^2+81x+2=0

a = -3; b = 81; c = +2;
Δ = b2-4ac
Δ = 812-4·(-3)·2
Δ = 6585
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{-(81)-\sqrt{6585}}{2*-3}=\frac{-81-\sqrt{6585}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+\sqrt{6585}}{2*-3}=\frac{-81+\sqrt{6585}}{-6}
$