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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


4x/12x^2+9x/12x^2-3+1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

13x-2*12x^2=0

Wy multiply elements

-24x^2+13x=0

a = -24; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-24)·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*-24}=\frac{-26}{-48}
=13/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-24}=\frac{0}{-48}
=0
$