5/4x+3/x=7

Solution for 5/4x+3/x=7 equation:

5/4x+3/x=7

We move all terms to the left:

5/4x+3/x-(7)=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+12x/4x^2-7=0

We multiply all the terms by the denominator


5x+12x-7*4x^2=0

We add all the numbers together, and all the variables

17x-7*4x^2=0

Wy multiply elements

-28x^2+17x=0

a = -28; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-28)·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*-28}=\frac{-34}{-56}
=17/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-28}=\frac{0}{-56}
=0
$