1/x=5/2x+4

Solution for 1/x=5/2x+4 equation:

1/x=5/2x+4

We move all terms to the left:

1/x-(5/2x+4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

1/x-5/2x-4=0

We calculate fractions


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

We multiply all the terms by the denominator


2x+(-5x)-4*2x^2=0

Wy multiply elements

-8x^2+2x+(-5x)=0

We get rid of parentheses

-8x^2+2x-5x=0

We add all the numbers together, and all the variables

-8x^2-3x=0

a = -8; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-8)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-8}=\frac{6}{-16}
=-3/8
$