5/x-3/4x=1

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

5/x-3/4x=1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


20x/4x^2+(-3x)/4x^2-1=0

We multiply all the terms by the denominator


20x+(-3x)-1*4x^2=0

Wy multiply elements

-4x^2+20x+(-3x)=0

We get rid of parentheses

-4x^2+20x-3x=0

We add all the numbers together, and all the variables

-4x^2+17x=0

a = -4; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-4)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-4}=\frac{-34}{-8}
=4+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-4}=\frac{0}{-8}
=0
$