1/2x+7=-4/3x-4

Solution for 1/2x+7=-4/3x-4 equation:

1/2x+7=-4/3x-4

We move all terms to the left:

1/2x+7-(-4/3x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/2x+4/3x+4+7=0

We calculate fractions


3x/6x^2+8x/6x^2+4+7=0

We add all the numbers together, and all the variables

3x/6x^2+8x/6x^2+11=0

We multiply all the terms by the denominator


3x+8x+11*6x^2=0

We add all the numbers together, and all the variables

11x+11*6x^2=0

Wy multiply elements

66x^2+11x=0

a = 66; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·66·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*66}=\frac{-22}{132}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*66}=\frac{0}{132}
=0
$