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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We use the square of the difference formula

x^2+22x-4+1=0

We add all the numbers together, and all the variables

x^2+22x-3=0

a = 1; b = 22; c = -3;
Δ = b2-4ac
Δ = 222-4·1·(-3)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-4\sqrt{31}}{2*1}=\frac{-22-4\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+4\sqrt{31}}{2*1}=\frac{-22+4\sqrt{31}}{2}
$