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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


21x/6x^2+(-4x)/6x^2-5-3=0

We add all the numbers together, and all the variables

21x/6x^2+(-4x)/6x^2-8=0

We multiply all the terms by the denominator


21x+(-4x)-8*6x^2=0

Wy multiply elements

-48x^2+21x+(-4x)=0

We get rid of parentheses

-48x^2+21x-4x=0

We add all the numbers together, and all the variables

-48x^2+17x=0

a = -48; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-48)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-48}=\frac{-34}{-96}
=17/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-48}=\frac{0}{-96}
=0
$