7/x=14/3x+4

Solution for 7/x=14/3x+4 equation:

7/x=14/3x+4

We move all terms to the left:

7/x-(14/3x+4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

7/x-14/3x-4=0

We calculate fractions


21x/3x^2+(-14x)/3x^2-4=0

We multiply all the terms by the denominator


21x+(-14x)-4*3x^2=0

Wy multiply elements

-12x^2+21x+(-14x)=0

We get rid of parentheses

-12x^2+21x-14x=0

We add all the numbers together, and all the variables

-12x^2+7x=0

a = -12; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-12)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-12}=\frac{-14}{-24}
=7/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-12}=\frac{0}{-24}
=0
$