7/2x=14/x-3

Solution for 7/2x=14/x-3 equation:

7/2x=14/x-3

We move all terms to the left:

7/2x-(14/x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x-3)!=0

x∈R


We get rid of parentheses

7/2x-14/x+3=0

We calculate fractions


7x/2x^2+(-28x)/2x^2+3=0

We multiply all the terms by the denominator


7x+(-28x)+3*2x^2=0

Wy multiply elements

6x^2+7x+(-28x)=0

We get rid of parentheses

6x^2+7x-28x=0

We add all the numbers together, and all the variables

6x^2-21x=0

a = 6; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·6·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*6}=\frac{42}{12}
=3+1/2
$