1=(7x+1)(7/x+1)

Solution for 1=(7x+1)(7/x+1) equation:

1=(7x+1)(7/x+1)

We move all terms to the left:

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


Domain of the equation: x+1))!=0

x∈R


We multiply parentheses ..

-((+49x^2+7x+7x+1))+1=0


We calculate terms in parentheses: -((+49x^2+7x+7x+1)), so:

(+49x^2+7x+7x+1)

We get rid of parentheses

49x^2+7x+7x+1

We add all the numbers together, and all the variables

49x^2+14x+1

Back to the equation:

-(49x^2+14x+1)


We get rid of parentheses

-49x^2-14x-1+1=0

We add all the numbers together, and all the variables

-49x^2-14x=0

a = -49; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-49)·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*-49}=\frac{0}{-98}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-49}=\frac{28}{-98}
=-2/7
$