1/x=x/5x+24

Solution for 1/x=x/5x+24 equation:

1/x=x/5x+24

We move all terms to the left:

1/x-(x/5x+24)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+24)!=0

x∈R


We get rid of parentheses

1/x-x/5x-24=0

We calculate fractions


(-1x^2)/5x^2+5x/5x^2-24=0

We multiply all the terms by the denominator


(-1x^2)+5x-24*5x^2=0

Wy multiply elements

(-1x^2)-120x^2+5x=0

We get rid of parentheses

-1x^2-120x^2+5x=0

We add all the numbers together, and all the variables

-121x^2+5x=0

a = -121; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-121)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-121}=\frac{-10}{-242}
=5/121
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-121}=\frac{0}{-242}
=0
$