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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-5x)/15x^2+(-6x)/15x^2-4+6=0

We add all the numbers together, and all the variables

(-5x)/15x^2+(-6x)/15x^2+2=0

We multiply all the terms by the denominator


(-5x)+(-6x)+2*15x^2=0

Wy multiply elements

30x^2+(-5x)+(-6x)=0

We get rid of parentheses

30x^2-5x-6x=0

We add all the numbers together, and all the variables

30x^2-11x=0

a = 30; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·30·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*30}=\frac{22}{60}
=11/30
$