1/4x-9/x=11

Solution for 1/4x-9/x=11 equation:

1/4x-9/x=11

We move all terms to the left:

1/4x-9/x-(11)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


x/4x^2+(-36x)/4x^2-11=0

We multiply all the terms by the denominator


x+(-36x)-11*4x^2=0

Wy multiply elements

-44x^2+x+(-36x)=0

We get rid of parentheses

-44x^2+x-36x=0

We add all the numbers together, and all the variables

-44x^2-35x=0

a = -44; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·(-44)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*-44}=\frac{0}{-88}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*-44}=\frac{70}{-88}
=-35/44
$