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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x-x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2+3x-1=0

a = 3; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·3·(-1)
Δ = 21
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{-(3)-\sqrt{21}}{2*3}=\frac{-3-\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{21}}{2*3}=\frac{-3+\sqrt{21}}{6}
$