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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


3x/15x^2+(-10x)/15x^2+4+3=0

We add all the numbers together, and all the variables

3x/15x^2+(-10x)/15x^2+7=0

We multiply all the terms by the denominator


3x+(-10x)+7*15x^2=0

Wy multiply elements

105x^2+3x+(-10x)=0

We get rid of parentheses

105x^2+3x-10x=0

We add all the numbers together, and all the variables

105x^2-7x=0

a = 105; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·105·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*105}=\frac{0}{210}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*105}=\frac{14}{210}
=1/15
$