28/3x-7=21/x+11

Solution for 28/3x-7=21/x+11 equation:

28/3x-7=21/x+11

We move all terms to the left:

28/3x-7-(21/x+11)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x+11)!=0

x∈R


We get rid of parentheses

28/3x-21/x-11-7=0

We calculate fractions


28x/3x^2+(-63x)/3x^2-11-7=0

We add all the numbers together, and all the variables

28x/3x^2+(-63x)/3x^2-18=0

We multiply all the terms by the denominator


28x+(-63x)-18*3x^2=0

Wy multiply elements

-54x^2+28x+(-63x)=0

We get rid of parentheses

-54x^2+28x-63x=0

We add all the numbers together, and all the variables

-54x^2-35x=0

a = -54; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·(-54)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*-54}=\frac{0}{-108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*-54}=\frac{70}{-108}
=-35/54
$