x+(x+1)/3x+17=1/2

Solution for x+(x+1)/3x+17=1/2 equation:

x+(x+1)/3x+17=1/2

We move all terms to the left:

x+(x+1)/3x+17-(1/2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+(x+1)/3x+17-(+1/2)=0

We get rid of parentheses

x+(x+1)/3x+17-1/2=0

We calculate fractions


x+(2x+2)/6x+(-3x)/6x+17=0

We multiply all the terms by the denominator


x*6x+(2x+2)+(-3x)+17*6x=0

Wy multiply elements

6x^2+(2x+2)+(-3x)+102x=0

We get rid of parentheses

6x^2+2x-3x+102x+2=0

We add all the numbers together, and all the variables

6x^2+101x+2=0

a = 6; b = 101; c = +2;
Δ = b2-4ac
Δ = 1012-4·6·2
Δ = 10153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(101)-\sqrt{10153}}{2*6}=\frac{-101-\sqrt{10153}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(101)+\sqrt{10153}}{2*6}=\frac{-101+\sqrt{10153}}{12}
$