1/2x+9x+2=1/2x+5

Solution for 1/2x+9x+2=1/2x+5 equation:

1/2x+9x+2=1/2x+5

We move all terms to the left:

1/2x+9x+2-(1/2x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We add all the numbers together, and all the variables

9x+1/2x-(1/2x+5)+2=0

We get rid of parentheses

9x+1/2x-1/2x-5+2=0

We multiply all the terms by the denominator


9x*2x-5*2x+2*2x+1-1=0

We add all the numbers together, and all the variables

9x*2x-5*2x+2*2x=0

Wy multiply elements

18x^2-10x+4x=0

We add all the numbers together, and all the variables

18x^2-6x=0

a = 18; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·18·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*18}=\frac{0}{36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*18}=\frac{12}{36}
=1/3
$