2x+9=18-1/2x

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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} $

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