(11/4x)+(7x/x+1)=7

Solution for (11/4x)+(7x/x+1)=7 equation:

(11/4x)+(7x/x+1)=7

We move all terms to the left:

(11/4x)+(7x/x+1)-(7)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x+1)!=0

x∈R


We add all the numbers together, and all the variables

(+11/4x)+(7x/x+1)-7=0

We get rid of parentheses

11/4x+7x/x+1-7=0

We calculate fractions


28x^2/4x^2+11x/4x^2+1-7=0

We add all the numbers together, and all the variables

28x^2/4x^2+11x/4x^2-6=0

We multiply all the terms by the denominator


28x^2+11x-6*4x^2=0

Wy multiply elements

28x^2-24x^2+11x=0

We add all the numbers together, and all the variables

4x^2+11x=0

a = 4; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·4·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*4}=\frac{-22}{8}
=-2+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*4}=\frac{0}{8}
=0
$