1/2x+13-9=x

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Solution for 1/2x+13-9=x equation:



1/2x+13-9=x
We move all terms to the left:
1/2x+13-9-(x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
-1x+1/2x+4=0
We multiply all the terms by the denominator
-1x*2x+4*2x+1=0
Wy multiply elements
-2x^2+8x+1=0
a = -2; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-2)·1
Δ = 72
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:
$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{2}}{2*-2}=\frac{-8-6\sqrt{2}}{-4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{2}}{2*-2}=\frac{-8+6\sqrt{2}}{-4} $

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