4x+3/3-x=5/6x

Solution for 4x+3/3-x=5/6x equation:

4x+3/3-x=5/6x

We move all terms to the left:

4x+3/3-x-(5/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-x-(+5/6x)+3/3=0

We add all the numbers together, and all the variables

3x-(+5/6x)+1=0

We get rid of parentheses

3x-5/6x+1=0

We multiply all the terms by the denominator


3x*6x+1*6x-5=0

Wy multiply elements

18x^2+6x-5=0

a = 18; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·18·(-5)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{11}}{2*18}=\frac{-6-6\sqrt{11}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{11}}{2*18}=\frac{-6+6\sqrt{11}}{36}
$