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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


4x/6x^2+(-15x)/6x^2-3-4=0

We add all the numbers together, and all the variables

4x/6x^2+(-15x)/6x^2-7=0

We multiply all the terms by the denominator


4x+(-15x)-7*6x^2=0

Wy multiply elements

-42x^2+4x+(-15x)=0

We get rid of parentheses

-42x^2+4x-15x=0

We add all the numbers together, and all the variables

-42x^2-11x=0

a = -42; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-42)·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*-42}=\frac{0}{-84}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-42}=\frac{22}{-84}
=-11/42
$