14+5/7x-20=4/x-4

Solution for 14+5/7x-20=4/x-4 equation:

14+5/7x-20=4/x-4

We move all terms to the left:

14+5/7x-20-(4/x-4)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We add all the numbers together, and all the variables

5/7x-(4/x-4)-6=0

We get rid of parentheses

5/7x-4/x+4-6=0

We calculate fractions


5x/7x^2+(-28x)/7x^2+4-6=0

We add all the numbers together, and all the variables

5x/7x^2+(-28x)/7x^2-2=0

We multiply all the terms by the denominator


5x+(-28x)-2*7x^2=0

Wy multiply elements

-14x^2+5x+(-28x)=0

We get rid of parentheses

-14x^2+5x-28x=0

We add all the numbers together, and all the variables

-14x^2-23x=0

a = -14; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-14)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-14}=\frac{0}{-28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-14}=\frac{46}{-28}
=-1+9/14
$