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x+1/2x=71
We move all terms to the left:
x+1/2x-(71)=0
Domain of the equation: 2x!=0We multiply all the terms by the denominator
x!=0/2
x!=0
x∈R
x*2x-71*2x+1=0
Wy multiply elements
2x^2-142x+1=0
a = 2; b = -142; c = +1;
Δ = b2-4ac
Δ = -1422-4·2·1
Δ = 20156
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20156}=\sqrt{4*5039}=\sqrt{4}*\sqrt{5039}=2\sqrt{5039}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-142)-2\sqrt{5039}}{2*2}=\frac{142-2\sqrt{5039}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-142)+2\sqrt{5039}}{2*2}=\frac{142+2\sqrt{5039}}{4} $
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