7/x-5-7/4x-20=-8

Solution for 7/x-5-7/4x-20=-8 equation:

7/x-5-7/4x-20=-8

We move all terms to the left:

7/x-5-7/4x-20-(-8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

7/x-7/4x-17=0

We calculate fractions


28x/4x^2+(-7x)/4x^2-17=0

We multiply all the terms by the denominator


28x+(-7x)-17*4x^2=0

Wy multiply elements

-68x^2+28x+(-7x)=0

We get rid of parentheses

-68x^2+28x-7x=0

We add all the numbers together, and all the variables

-68x^2+21x=0

a = -68; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-68)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-68}=\frac{-42}{-136}
=21/68
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-68}=\frac{0}{-136}
=0
$