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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

13x+3*12x^2=0

Wy multiply elements

36x^2+13x=0

a = 36; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·36·0
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*36}=\frac{-26}{72}
=-13/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*36}=\frac{0}{72}
=0
$