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x-186/x=2
We move all terms to the left:
x-186/x-(2)=0
Domain of the equation: x!=0We multiply all the terms by the denominator
x∈R
x*x-2*x-186=0
We add all the numbers together, and all the variables
-2x+x*x-186=0
Wy multiply elements
x^2-2x-186=0
a = 1; b = -2; c = -186;
Δ = b2-4ac
Δ = -22-4·1·(-186)
Δ = 748
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{748}=\sqrt{4*187}=\sqrt{4}*\sqrt{187}=2\sqrt{187}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{187}}{2*1}=\frac{2-2\sqrt{187}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{187}}{2*1}=\frac{2+2\sqrt{187}}{2} $
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