2x+9=18-1/2x

Solution for 2x+9=18-1/2x equation:

2x+9=18-1/2x

We move all terms to the left:

2x+9-(18-1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(-1/2x+18)+9=0

We get rid of parentheses

2x+1/2x-18+9=0

We multiply all the terms by the denominator


2x*2x-18*2x+9*2x+1=0

Wy multiply elements

4x^2-36x+18x+1=0

We add all the numbers together, and all the variables

4x^2-18x+1=0

a = 4; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·4·1
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{77}}{2*4}=\frac{18-2\sqrt{77}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{77}}{2*4}=\frac{18+2\sqrt{77}}{8}
$