x+1=1/22x+8

Solution for x+1=1/22x+8 equation:

x+1=1/22x+8

We move all terms to the left:

x+1-(1/22x+8)=0


Domain of the equation: 22x+8)!=0

x∈R


We get rid of parentheses

x-1/22x-8+1=0

We multiply all the terms by the denominator


x*22x-8*22x+1*22x-1=0

Wy multiply elements

22x^2-176x+22x-1=0

We add all the numbers together, and all the variables

22x^2-154x-1=0

a = 22; b = -154; c = -1;
Δ = b2-4ac
Δ = -1542-4·22·(-1)
Δ = 23804
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:

$\sqrt{\Delta}=\sqrt{23804}=\sqrt{4*5951}=\sqrt{4}*\sqrt{5951}=2\sqrt{5951}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-154)-2\sqrt{5951}}{2*22}=\frac{154-2\sqrt{5951}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-154)+2\sqrt{5951}}{2*22}=\frac{154+2\sqrt{5951}}{44}
$