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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


15x/24x^2+56x/24x^2+(-9x)/24x^2-3=0

We multiply all the terms by the denominator


15x+56x+(-9x)-3*24x^2=0

We add all the numbers together, and all the variables

71x+(-9x)-3*24x^2=0

Wy multiply elements

-72x^2+71x+(-9x)=0

We get rid of parentheses

-72x^2+71x-9x=0

We add all the numbers together, and all the variables

-72x^2+62x=0

a = -72; b = 62; c = 0;
Δ = b2-4ac
Δ = 622-4·(-72)·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-62}{2*-72}=\frac{-124}{-144}
=31/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+62}{2*-72}=\frac{0}{-144}
=0
$