1/x+7x=-8

Solution for 1/x+7x=-8 equation:

1/x+7x=-8

We move all terms to the left:

1/x+7x-(-8)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

7x+1/x+8=0

We multiply all the terms by the denominator


7x*x+8*x+1=0

We add all the numbers together, and all the variables

8x+7x*x+1=0

Wy multiply elements

7x^2+8x+1=0

a = 7; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·7·1
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6}{2*7}=\frac{-14}{14}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6}{2*7}=\frac{-2}{14}
=-1/7
$