X+x+2/4x=22

Solution for X+x+2/4x=22 equation:

X+X+2/4X=22

We move all terms to the left:

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


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We add all the numbers together, and all the variables

2X+2/4X-22=0

We multiply all the terms by the denominator


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

Wy multiply elements

8X^2-88X+2=0

a = 8; b = -88; c = +2;
Δ = b2-4ac
Δ = -882-4·8·2
Δ = 7680
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:

$\sqrt{\Delta}=\sqrt{7680}=\sqrt{256*30}=\sqrt{256}*\sqrt{30}=16\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-16\sqrt{30}}{2*8}=\frac{88-16\sqrt{30}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+16\sqrt{30}}{2*8}=\frac{88+16\sqrt{30}}{16}
$