5/4x-6/x-1=0

Solution for 5/4x-6/x-1=0 equation:

5/4x-6/x-1=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


5x/4x^2+(-24x)/4x^2-1=0

We multiply all the terms by the denominator


5x+(-24x)-1*4x^2=0

Wy multiply elements

-4x^2+5x+(-24x)=0

We get rid of parentheses

-4x^2+5x-24x=0

We add all the numbers together, and all the variables

-4x^2-19x=0

a = -4; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-4)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-4}=\frac{38}{-8}
=-4+3/4
$