2x-6/x=22

Solution for 2x-6/x=22 equation:

2x-6/x=22

We move all terms to the left:

2x-6/x-(22)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-22*x-6=0

We add all the numbers together, and all the variables

-22x+2x*x-6=0

Wy multiply elements

2x^2-22x-6=0

a = 2; b = -22; c = -6;
Δ = b2-4ac
Δ = -222-4·2·(-6)
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{133}}{2*2}=\frac{22-2\sqrt{133}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{133}}{2*2}=\frac{22+2\sqrt{133}}{4}
$