1/3x+5=-3/4x-7

Solution for 1/3x+5=-3/4x-7 equation:

1/3x+5=-3/4x-7

We move all terms to the left:

1/3x+5-(-3/4x-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-7)!=0

x∈R


We get rid of parentheses

1/3x+3/4x+7+5=0

We calculate fractions


4x/12x^2+9x/12x^2+7+5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

13x+12*12x^2=0

Wy multiply elements

144x^2+13x=0

a = 144; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·144·0
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*144}=\frac{-26}{288}
=-13/144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*144}=\frac{0}{288}
=0
$