X/3x+4-x=6

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

X/3X+4-X=6

We move all terms to the left:

X/3X+4-X-(6)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

-1X+X/3X-2=0

We multiply all the terms by the denominator


-1X*3X+X-2*3X=0

We add all the numbers together, and all the variables

X-1X*3X-2*3X=0

Wy multiply elements

-3X^2+X-6X=0

We add all the numbers together, and all the variables

-3X^2-5X=0

a = -3; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-3)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-3}=\frac{0}{-6}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-3}=\frac{10}{-6}
=-1+2/3
$