1/x+8=7x

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

1/x+8=7x

We move all terms to the left:

1/x+8-(7x)=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 = 92
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{23}}{2*-7}=\frac{-8-2\sqrt{23}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{23}}{2*-7}=\frac{-8+2\sqrt{23}}{-14}
$