5/x-7+7/3x-21=10

Solution for 5/x-7+7/3x-21=10 equation:

5/x-7+7/3x-21=10

We move all terms to the left:

5/x-7+7/3x-21-(10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/x+7/3x-38=0

We calculate fractions


15x/3x^2+7x/3x^2-38=0

We multiply all the terms by the denominator


15x+7x-38*3x^2=0

We add all the numbers together, and all the variables

22x-38*3x^2=0

Wy multiply elements

-114x^2+22x=0

a = -114; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-114)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-114}=\frac{-44}{-228}
=11/57
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-114}=\frac{0}{-228}
=0
$