7x+2=9/x=-1

Solution for 7x+2=9/x=-1 equation:

7x+2=9/x=-1

We move all terms to the left:

7x+2-(9/x)=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-(+9/x)+2=0

We get rid of parentheses

7x-9/x+2=0

We multiply all the terms by the denominator


7x*x+2*x-9=0

We add all the numbers together, and all the variables

2x+7x*x-9=0

Wy multiply elements

7x^2+2x-9=0

a = 7; b = 2; c = -9;
Δ = b2-4ac
Δ = 22-4·7·(-9)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-16}{2*7}=\frac{-18}{14}
=-1+2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+16}{2*7}=\frac{14}{14}
=1
$