4/x-3-4/7x-21=-2

Solution for 4/x-3-4/7x-21=-2 equation:

4/x-3-4/7x-21=-2

We move all terms to the left:

4/x-3-4/7x-21-(-2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

4/x-4/7x-22=0

We calculate fractions


28x/7x^2+(-4x)/7x^2-22=0

We multiply all the terms by the denominator


28x+(-4x)-22*7x^2=0

Wy multiply elements

-154x^2+28x+(-4x)=0

We get rid of parentheses

-154x^2+28x-4x=0

We add all the numbers together, and all the variables

-154x^2+24x=0

a = -154; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-154)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-154}=\frac{-48}{-308}
=12/77
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-154}=\frac{0}{-308}
=0
$