5/2x-4=6-7/3x

Solution for 5/2x-4=6-7/3x equation:

5/2x-4=6-7/3x

We move all terms to the left:

5/2x-4-(6-7/3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-(-7/3x+6)-4=0

We get rid of parentheses

5/2x+7/3x-6-4=0

We calculate fractions


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

We add all the numbers together, and all the variables

15x/6x^2+14x/6x^2-10=0

We multiply all the terms by the denominator


15x+14x-10*6x^2=0

We add all the numbers together, and all the variables

29x-10*6x^2=0

Wy multiply elements

-60x^2+29x=0

a = -60; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-60)·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*-60}=\frac{-58}{-120}
=29/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-60}=\frac{0}{-120}
=0
$