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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-28x^2)/128x^2+256x/128x^2+192x/128x^2=0

We multiply all the terms by the denominator


(-28x^2)+256x+192x=0

We add all the numbers together, and all the variables

(-28x^2)+448x=0

We get rid of parentheses

-28x^2+448x=0

a = -28; b = 448; c = 0;
Δ = b2-4ac
Δ = 4482-4·(-28)·0
Δ = 200704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{200704}=448$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(448)-448}{2*-28}=\frac{-896}{-56}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(448)+448}{2*-28}=\frac{0}{-56}
=0
$