3/4x+6/x=1

Solution for 3/4x+6/x=1 equation:

3/4x+6/x=1

We move all terms to the left:

3/4x+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


3x/4x^2+24x/4x^2-1=0

We multiply all the terms by the denominator


3x+24x-1*4x^2=0

We add all the numbers together, and all the variables

27x-1*4x^2=0

Wy multiply elements

-4x^2+27x=0

a = -4; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-4)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-4}=\frac{-54}{-8}
=6+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-4}=\frac{0}{-8}
=0
$