x^-14=8/x

Solution for x^-14=8/x equation:

x^-14=8/x

We move all terms to the left:

x^-14-(8/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

x^-(+8/x)-14=0

We add all the numbers together, and all the variables

x-(+8/x)-14=0

We get rid of parentheses

x-8/x-14=0

We multiply all the terms by the denominator


x*x-14*x-8=0

We add all the numbers together, and all the variables

-14x+x*x-8=0

Wy multiply elements

x^2-14x-8=0

a = 1; b = -14; c = -8;
Δ = b2-4ac
Δ = -142-4·1·(-8)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{57}}{2*1}=\frac{14-2\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{57}}{2*1}=\frac{14+2\sqrt{57}}{2}
$