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2/x+5x=10
We move all terms to the left:
2/x+5x-(10)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
5x+2/x-10=0
We multiply all the terms by the denominator
5x*x-10*x+2=0
We add all the numbers together, and all the variables
-10x+5x*x+2=0
Wy multiply elements
5x^2-10x+2=0
a = 5; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·5·2
Δ = 60
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{15}}{2*5}=\frac{10-2\sqrt{15}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{15}}{2*5}=\frac{10+2\sqrt{15}}{10} $
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