5/7x-1/2x=3

Solution for 5/7x-1/2x=3 equation:

5/7x-1/2x=3

We move all terms to the left:

5/7x-1/2x-(3)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


10x/14x^2+(-7x)/14x^2-3=0

We multiply all the terms by the denominator


10x+(-7x)-3*14x^2=0

Wy multiply elements

-42x^2+10x+(-7x)=0

We get rid of parentheses

-42x^2+10x-7x=0

We add all the numbers together, and all the variables

-42x^2+3x=0

a = -42; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-42)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-42}=\frac{-6}{-84}
=1/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-42}=\frac{0}{-84}
=0
$