3/x-1-5/4x-4=18

Solution for 3/x-1-5/4x-4=18 equation:

3/x-1-5/4x-4=18

We move all terms to the left:

3/x-1-5/4x-4-(18)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/x-5/4x-23=0

We calculate fractions


12x/4x^2+(-5x)/4x^2-23=0

We multiply all the terms by the denominator


12x+(-5x)-23*4x^2=0

Wy multiply elements

-92x^2+12x+(-5x)=0

We get rid of parentheses

-92x^2+12x-5x=0

We add all the numbers together, and all the variables

-92x^2+7x=0

a = -92; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-92)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-92}=\frac{-14}{-184}
=7/92
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-92}=\frac{0}{-184}
=0
$