1/3x+2=12/19x-3

Solution for 1/3x+2=12/19x-3 equation:

1/3x+2=12/19x-3

We move all terms to the left:

1/3x+2-(12/19x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 19x-3)!=0

x∈R


We get rid of parentheses

1/3x-12/19x+3+2=0

We calculate fractions


19x/57x^2+(-36x)/57x^2+3+2=0

We add all the numbers together, and all the variables

19x/57x^2+(-36x)/57x^2+5=0

We multiply all the terms by the denominator


19x+(-36x)+5*57x^2=0

Wy multiply elements

285x^2+19x+(-36x)=0

We get rid of parentheses

285x^2+19x-36x=0

We add all the numbers together, and all the variables

285x^2-17x=0

a = 285; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·285·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*285}=\frac{0}{570}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*285}=\frac{34}{570}
=17/285
$