3/2x-1/2=3/5x-19

Solution for 3/2x-1/2=3/5x-19 equation:

3/2x-1/2=3/5x-19

We move all terms to the left:

3/2x-1/2-(3/5x-19)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x-19)!=0

x∈R


We get rid of parentheses

3/2x-3/5x+19-1/2=0

We calculate fractions


15x/40x^2+(-24x)/40x^2+(-5x)/40x^2+19=0

We multiply all the terms by the denominator


15x+(-24x)+(-5x)+19*40x^2=0

Wy multiply elements

760x^2+15x+(-24x)+(-5x)=0

We get rid of parentheses

760x^2+15x-24x-5x=0

We add all the numbers together, and all the variables

760x^2-14x=0

a = 760; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·760·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*760}=\frac{0}{1520}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*760}=\frac{28}{1520}
=7/380
$