9/4x-5/x+13=0

Solution for 9/4x-5/x+13=0 equation:

9/4x-5/x+13=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


9x/4x^2+(-20x)/4x^2+13=0

We multiply all the terms by the denominator


9x+(-20x)+13*4x^2=0

Wy multiply elements

52x^2+9x+(-20x)=0

We get rid of parentheses

52x^2+9x-20x=0

We add all the numbers together, and all the variables

52x^2-11x=0

a = 52; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·52·0
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*52}=\frac{0}{104}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*52}=\frac{22}{104}
=11/52
$