4/x-5=8x

Solution for 4/x-5=8x equation:

4/x-5=8x

We move all terms to the left:

4/x-5-(8x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-8x+4/x-5=0

We multiply all the terms by the denominator


-8x*x-5*x+4=0

We add all the numbers together, and all the variables

-5x-8x*x+4=0

Wy multiply elements

-8x^2-5x+4=0

a = -8; b = -5; c = +4;
Δ = b2-4ac
Δ = -52-4·(-8)·4
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{17}}{2*-8}=\frac{5-3\sqrt{17}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{17}}{2*-8}=\frac{5+3\sqrt{17}}{-16}
$