1/2x-x+5=0

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Solution for 1/2x-x+5=0 equation:



1/2x-x+5=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+5=0
We multiply all the terms by the denominator
-1x*2x+5*2x+1=0
Wy multiply elements
-2x^2+10x+1=0
a = -2; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-2)·1
Δ = 108
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:
$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{3}}{2*-2}=\frac{-10-6\sqrt{3}}{-4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{3}}{2*-2}=\frac{-10+6\sqrt{3}}{-4} $

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