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(8/x)-x=4
We move all terms to the left:
(8/x)-x-(4)=0
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+8/x)-x-4=0
We add all the numbers together, and all the variables
-1x+(+8/x)-4=0
We get rid of parentheses
-1x+8/x-4=0
We multiply all the terms by the denominator
-1x*x-4*x+8=0
We add all the numbers together, and all the variables
-4x-1x*x+8=0
Wy multiply elements
-1x^2-4x+8=0
a = -1; b = -4; c = +8;
Δ = b2-4ac
Δ = -42-4·(-1)·8
Δ = 48
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{3}}{2*-1}=\frac{4-4\sqrt{3}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{3}}{2*-1}=\frac{4+4\sqrt{3}}{-2} $
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