)8/x+x/2=5

Solution for )8/x+x/2=5 equation:

)8/x+x/2=5

We move all terms to the left:

)8/x+x/2-(5)=0


Domain of the equation: x!=0

x∈R


We calculate fractions


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
$