6-4/3x+1/3=1/2x+5

Solution for 6-4/3x+1/3=1/2x+5 equation:

6-4/3x+1/3=1/2x+5

We move all terms to the left:

6-4/3x+1/3-(1/2x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

-4/3x-1/2x-5+6+1/3=0

We calculate fractions


(-8x)/54x^2+(-27x)/54x^2+2x/54x^2-5+6=0

We add all the numbers together, and all the variables

(-8x)/54x^2+(-27x)/54x^2+2x/54x^2+1=0

We multiply all the terms by the denominator


(-8x)+(-27x)+2x+1*54x^2=0

We add all the numbers together, and all the variables

2x+(-8x)+(-27x)+1*54x^2=0

Wy multiply elements

54x^2+2x+(-8x)+(-27x)=0

We get rid of parentheses

54x^2+2x-8x-27x=0

We add all the numbers together, and all the variables

54x^2-33x=0

a = 54; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·54·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*54}=\frac{0}{108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*54}=\frac{66}{108}
=11/18
$