1/x=x/7x+44

Solution for 1/x=x/7x+44 equation:

1/x=x/7x+44

We move all terms to the left:

1/x-(x/7x+44)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x+44)!=0

x∈R


We get rid of parentheses

1/x-x/7x-44=0

We calculate fractions


(-1x^2)/7x^2+7x/7x^2-44=0

We multiply all the terms by the denominator


(-1x^2)+7x-44*7x^2=0

Wy multiply elements

(-1x^2)-308x^2+7x=0

We get rid of parentheses

-1x^2-308x^2+7x=0

We add all the numbers together, and all the variables

-309x^2+7x=0

a = -309; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-309)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-309}=\frac{-14}{-618}
=7/309
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-309}=\frac{0}{-618}
=0
$