1/x-24/7x-3=0

Solution for 1/x-24/7x-3=0 equation:

1/x-24/7x-3=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We calculate fractions


7x/7x^2+(-24x)/7x^2-3=0

We multiply all the terms by the denominator


7x+(-24x)-3*7x^2=0

Wy multiply elements

-21x^2+7x+(-24x)=0

We get rid of parentheses

-21x^2+7x-24x=0

We add all the numbers together, and all the variables

-21x^2-17x=0

a = -21; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·(-21)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*-21}=\frac{34}{-42}
=-17/21
$