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

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

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

We move all terms to the left:

4/2x-3-(7/3x-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

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

We calculate fractions


12x/6x^2+(-14x)/6x^2+5-3=0

We add all the numbers together, and all the variables

12x/6x^2+(-14x)/6x^2+2=0

We multiply all the terms by the denominator


12x+(-14x)+2*6x^2=0

Wy multiply elements

12x^2+12x+(-14x)=0

We get rid of parentheses

12x^2+12x-14x=0

We add all the numbers together, and all the variables

12x^2-2x=0

a = 12; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·12·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*12}=\frac{4}{24}
=1/6
$