8x-47=6/x

Solution for 8x-47=6/x equation:

8x-47=6/x

We move all terms to the left:

8x-47-(6/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

8x-(+6/x)-47=0

We get rid of parentheses

8x-6/x-47=0

We multiply all the terms by the denominator


8x*x-47*x-6=0

We add all the numbers together, and all the variables

-47x+8x*x-6=0

Wy multiply elements

8x^2-47x-6=0

a = 8; b = -47; c = -6;
Δ = b2-4ac
Δ = -472-4·8·(-6)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-49}{2*8}=\frac{-2}{16}
=-1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+49}{2*8}=\frac{96}{16}
=6
$