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

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

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

We move all terms to the left:

5/2x-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

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-98x^2+29x=0

a = -98; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-98)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-98}=\frac{-58}{-196}
=29/98
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-98}=\frac{0}{-196}
=0
$