7/3x-1=5/2x+4

Solution for 7/3x-1=5/2x+4 equation:

7/3x-1=5/2x+4

We move all terms to the left:

7/3x-1-(5/2x+4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

7/3x-5/2x-4-1=0

We calculate fractions


14x/6x^2+(-15x)/6x^2-4-1=0

We add all the numbers together, and all the variables

14x/6x^2+(-15x)/6x^2-5=0

We multiply all the terms by the denominator


14x+(-15x)-5*6x^2=0

Wy multiply elements

-30x^2+14x+(-15x)=0

We get rid of parentheses

-30x^2+14x-15x=0

We add all the numbers together, and all the variables

-30x^2-1x=0

a = -30; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-30)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-30}=\frac{0}{-60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-30}=\frac{2}{-60}
=-1/30
$