1/x+8(x+9)=1

Solution for 1/x+8(x+9)=1 equation:

1/x+8(x+9)=1

We move all terms to the left:

1/x+8(x+9)-(1)=0


Domain of the equation: x!=0

x∈R


We multiply parentheses

1/x+8x+72-1=0

We multiply all the terms by the denominator


8x*x+72*x-1*x+1=0

We add all the numbers together, and all the variables

71x+8x*x+1=0

Wy multiply elements

8x^2+71x+1=0

a = 8; b = 71; c = +1;
Δ = b2-4ac
Δ = 712-4·8·1
Δ = 5009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(71)-\sqrt{5009}}{2*8}=\frac{-71-\sqrt{5009}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(71)+\sqrt{5009}}{2*8}=\frac{-71+\sqrt{5009}}{16}
$