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)8/x+x/2=5
We move all terms to the left:
)8/x+x/2-(5)=0
Domain of the equation: x!=0We calculate fractions
x∈R
x^2/2x+()/2x-5=0
We multiply all the terms by the denominator
x^2-5*2x+()=0
We add all the numbers together, and all the variables
x^2-5*2x=0
Wy multiply elements
x^2-10x=0
a = 1; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·1·0
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*1}=\frac{0}{2} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*1}=\frac{20}{2} =10 $
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