7/4x+3/x=1

Solution for 7/4x+3/x=1 equation:

7/4x+3/x=1

We move all terms to the left:

7/4x+3/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


7x/4x^2+12x/4x^2-1=0

We multiply all the terms by the denominator


7x+12x-1*4x^2=0

We add all the numbers together, and all the variables

19x-1*4x^2=0

Wy multiply elements

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