2/x+3/8=7/2x

Solution for 2/x+3/8=7/2x equation:

2/x+3/8=7/2x

We move all terms to the left:

2/x+3/8-(7/2x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/x-(+7/2x)+3/8=0

We get rid of parentheses

2/x-7/2x+3/8=0

We calculate fractions


12x^2/128x^2+256x/128x^2+(-448x)/128x^2=0

We multiply all the terms by the denominator


12x^2+256x+(-448x)=0

We get rid of parentheses

12x^2+256x-448x=0

We add all the numbers together, and all the variables

12x^2-192x=0

a = 12; b = -192; c = 0;
Δ = b2-4ac
Δ = -1922-4·12·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-192}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+192}{2*12}=\frac{384}{24}
=16
$