4x-8/x=122

Solution for 4x-8/x=122 equation:

4x-8/x=122

We move all terms to the left:

4x-8/x-(122)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


4x*x-122*x-8=0

We add all the numbers together, and all the variables

-122x+4x*x-8=0

Wy multiply elements

4x^2-122x-8=0

a = 4; b = -122; c = -8;
Δ = b2-4ac
Δ = -1222-4·4·(-8)
Δ = 15012
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:

$\sqrt{\Delta}=\sqrt{15012}=\sqrt{36*417}=\sqrt{36}*\sqrt{417}=6\sqrt{417}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-122)-6\sqrt{417}}{2*4}=\frac{122-6\sqrt{417}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-122)+6\sqrt{417}}{2*4}=\frac{122+6\sqrt{417}}{8}
$