3/x+5/4x=4

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

3/x+5/4x=4

We move all terms to the left:

3/x+5/4x-(4)=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


12x/4x^2+5x/4x^2-4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

17x-4*4x^2=0

Wy multiply elements

-16x^2+17x=0

a = -16; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-16)·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*-16}=\frac{-34}{-32}
=1+1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-16}=\frac{0}{-32}
=0
$