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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


35x^2/14x^2+(-6x)/14x^2-4-3=0

We add all the numbers together, and all the variables

35x^2/14x^2+(-6x)/14x^2-7=0

We multiply all the terms by the denominator


35x^2+(-6x)-7*14x^2=0

Wy multiply elements

35x^2-98x^2+(-6x)=0

We get rid of parentheses

35x^2-98x^2-6x=0

We add all the numbers together, and all the variables

-63x^2-6x=0

a = -63; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-63)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-63}=\frac{0}{-126}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-63}=\frac{12}{-126}
=-2/21
$