4/x+8/4x=12

Solution for 4/x+8/4x=12 equation:

4/x+8/4x=12

We move all terms to the left:

4/x+8/4x-(12)=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


16x/4x^2+8x/4x^2-12=0

We multiply all the terms by the denominator


16x+8x-12*4x^2=0

We add all the numbers together, and all the variables

24x-12*4x^2=0

Wy multiply elements

-48x^2+24x=0

a = -48; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-48)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-48}=\frac{-48}{-96}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-48}=\frac{0}{-96}
=0
$