x+9=1/2(2x)

Solution for x+9=1/2(2x) equation:

x+9=1/2(2x)

We move all terms to the left:

x+9-(1/2(2x))=0


Domain of the equation: 22x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+1/22x)+9=0

We get rid of parentheses

x-1/22x+9=0

We multiply all the terms by the denominator


x*22x+9*22x-1=0

Wy multiply elements

22x^2+198x-1=0

a = 22; b = 198; c = -1;
Δ = b2-4ac
Δ = 1982-4·22·(-1)
Δ = 39292
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:

$\sqrt{\Delta}=\sqrt{39292}=\sqrt{4*9823}=\sqrt{4}*\sqrt{9823}=2\sqrt{9823}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(198)-2\sqrt{9823}}{2*22}=\frac{-198-2\sqrt{9823}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(198)+2\sqrt{9823}}{2*22}=\frac{-198+2\sqrt{9823}}{44}
$