3/x+8/4x=5

Solution for 3/x+8/4x=5 equation:

3/x+8/4x=5

We move all terms to the left:

3/x+8/4x-(5)=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+8x/4x^2-5=0

We multiply all the terms by the denominator


12x+8x-5*4x^2=0

We add all the numbers together, and all the variables

20x-5*4x^2=0

Wy multiply elements

-20x^2+20x=0

a = -20; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-20)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-20}=\frac{-40}{-40}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-20}=\frac{0}{-40}
=0
$