69/x+4=162/2x

Solution for 69/x+4=162/2x equation:

69/x+4=162/2x

We move all terms to the left:

69/x+4-(162/2x)=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

69/x-(+162/2x)+4=0

We get rid of parentheses

69/x-162/2x+4=0

We calculate fractions


138x/2x^2+(-162x)/2x^2+4=0

We multiply all the terms by the denominator


138x+(-162x)+4*2x^2=0

Wy multiply elements

8x^2+138x+(-162x)=0

We get rid of parentheses

8x^2+138x-162x=0

We add all the numbers together, and all the variables

8x^2-24x=0

a = 8; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·8·0
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*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*8}=\frac{48}{16}
=3
$