2/x=x/7x-24

Solution for 2/x=x/7x-24 equation:

2/x=x/7x-24

We move all terms to the left:

2/x-(x/7x-24)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x-24)!=0

x∈R


We get rid of parentheses

2/x-x/7x+24=0

We calculate fractions


(-1x^2)/7x^2+14x/7x^2+24=0

We multiply all the terms by the denominator


(-1x^2)+14x+24*7x^2=0

Wy multiply elements

(-1x^2)+168x^2+14x=0

We get rid of parentheses

-1x^2+168x^2+14x=0

We add all the numbers together, and all the variables

167x^2+14x=0

a = 167; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·167·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*167}=\frac{-28}{334}
=-14/167
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*167}=\frac{0}{334}
=0
$