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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


9x/12x^2+4x/12x^2+2+3=0

We add all the numbers together, and all the variables

9x/12x^2+4x/12x^2+5=0

We multiply all the terms by the denominator


9x+4x+5*12x^2=0

We add all the numbers together, and all the variables

13x+5*12x^2=0

Wy multiply elements

60x^2+13x=0

a = 60; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·60·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*60}=\frac{-26}{120}
=-13/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*60}=\frac{0}{120}
=0
$