4/3x+1=2x+5+x

Solution for 4/3x+1=2x+5+x equation:

4/3x+1=2x+5+x

We move all terms to the left:

4/3x+1-(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

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

We get rid of parentheses

4/3x-3x-5+1=0

We multiply all the terms by the denominator


-3x*3x-5*3x+1*3x+4=0

Wy multiply elements

-9x^2-15x+3x+4=0

We add all the numbers together, and all the variables

-9x^2-12x+4=0

a = -9; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·(-9)·4
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{2}}{2*-9}=\frac{12-12\sqrt{2}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{2}}{2*-9}=\frac{12+12\sqrt{2}}{-18}
$