3/x+1+4/x-7=29/4x-1

Solution for 3/x+1+4/x-7=29/4x-1 equation:

3/x+1+4/x-7=29/4x-1

We move all terms to the left:

3/x+1+4/x-7-(29/4x-1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x-1)!=0

x∈R


We add all the numbers together, and all the variables

3/x+4/x-(29/4x-1)-6=0

We get rid of parentheses

3/x+4/x-29/4x+1-6=0

We calculate fractions


(16x+3)/4x^2+(-29x)/4x^2+1-6=0

We add all the numbers together, and all the variables

(16x+3)/4x^2+(-29x)/4x^2-5=0

We multiply all the terms by the denominator


(16x+3)+(-29x)-5*4x^2=0

Wy multiply elements

-20x^2+(16x+3)+(-29x)=0

We get rid of parentheses

-20x^2+16x-29x+3=0

We add all the numbers together, and all the variables

-20x^2-13x+3=0

a = -20; b = -13; c = +3;
Δ = b2-4ac
Δ = -132-4·(-20)·3
Δ = 409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{409}}{2*-20}=\frac{13-\sqrt{409}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{409}}{2*-20}=\frac{13+\sqrt{409}}{-40}
$