3/7x+4=3/2x-1

Solution for 3/7x+4=3/2x-1 equation:

3/7x+4=3/2x-1

We move all terms to the left:

3/7x+4-(3/2x-1)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

3/7x-3/2x+1+4=0

We calculate fractions


6x/14x^2+(-21x)/14x^2+1+4=0

We add all the numbers together, and all the variables

6x/14x^2+(-21x)/14x^2+5=0

We multiply all the terms by the denominator


6x+(-21x)+5*14x^2=0

Wy multiply elements

70x^2+6x+(-21x)=0

We get rid of parentheses

70x^2+6x-21x=0

We add all the numbers together, and all the variables

70x^2-15x=0

a = 70; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·70·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*70}=\frac{0}{140}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*70}=\frac{30}{140}
=3/14
$