4+8/x=x+6

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Solution for 4+8/x=x+6 equation:



4+8/x=x+6
We move all terms to the left:
4+8/x-(x+6)=0
Domain of the equation: x!=0
x∈R
We get rid of parentheses
8/x-x-6+4=0
We multiply all the terms by the denominator
-x*x-6*x+4*x+8=0
We add all the numbers together, and all the variables
-2x-x*x+8=0
Wy multiply elements
-1x^2-2x+8=0
a = -1; b = -2; c = +8;
Δ = b2-4ac
Δ = -22-4·(-1)·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*-1}=\frac{-4}{-2} =+2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*-1}=\frac{8}{-2} =-4 $

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