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x-2/x=54
We move all terms to the left:
x-2/x-(54)=0
Domain of the equation: x!=0We multiply all the terms by the denominator
x∈R
x*x-54*x-2=0
We add all the numbers together, and all the variables
-54x+x*x-2=0
Wy multiply elements
x^2-54x-2=0
a = 1; b = -54; c = -2;
Δ = b2-4ac
Δ = -542-4·1·(-2)
Δ = 2924
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2924}=\sqrt{4*731}=\sqrt{4}*\sqrt{731}=2\sqrt{731}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{731}}{2*1}=\frac{54-2\sqrt{731}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{731}}{2*1}=\frac{54+2\sqrt{731}}{2} $
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