2+4(x-1)=22/x=

Solution for 2+4(x-1)=22/x= equation:

2+4(x-1)=22/x=

We move all terms to the left:

2+4(x-1)-(22/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

4(x-1)-(+22/x)+2=0

We multiply parentheses

4x-(+22/x)-4+2=0

We get rid of parentheses

4x-22/x-4+2=0

We multiply all the terms by the denominator


4x*x-4*x+2*x-22=0

We add all the numbers together, and all the variables

-2x+4x*x-22=0

Wy multiply elements

4x^2-2x-22=0

a = 4; b = -2; c = -22;
Δ = b2-4ac
Δ = -22-4·4·(-22)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{89}}{2*4}=\frac{2-2\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{89}}{2*4}=\frac{2+2\sqrt{89}}{8}
$