8/2x+3x=28

Solution for 8/2x+3x=28 equation:

8/2x+3x=28

We move all terms to the left:

8/2x+3x-(28)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+8/2x-28=0

We multiply all the terms by the denominator


3x*2x-28*2x+8=0

Wy multiply elements

6x^2-56x+8=0

a = 6; b = -56; c = +8;
Δ = b2-4ac
Δ = -562-4·6·8
Δ = 2944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{46}}{2*6}=\frac{56-8\sqrt{46}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{46}}{2*6}=\frac{56+8\sqrt{46}}{12}
$