7x-(5/x)=2

Solution for 7x-(5/x)=2 equation:

7x-(5/x)=2

We move all terms to the left:

7x-(5/x)-(2)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x-(+5/x)-2=0

We get rid of parentheses

7x-5/x-2=0

We multiply all the terms by the denominator


7x*x-2*x-5=0

We add all the numbers together, and all the variables

-2x+7x*x-5=0

Wy multiply elements

7x^2-2x-5=0

a = 7; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·7·(-5)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-12}{2*7}=\frac{-10}{14}
=-5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12}{2*7}=\frac{14}{14}
=1
$