(48/x)+2x=22

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Solution for (48/x)+2x=22 equation:



(48/x)+2x=22
We move all terms to the left:
(48/x)+2x-(22)=0
Domain of the equation: x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+48/x)+2x-22=0
We add all the numbers together, and all the variables
2x+(+48/x)-22=0
We get rid of parentheses
2x+48/x-22=0
We multiply all the terms by the denominator
2x*x-22*x+48=0
We add all the numbers together, and all the variables
-22x+2x*x+48=0
Wy multiply elements
2x^2-22x+48=0
a = 2; b = -22; c = +48;
Δ = b2-4ac
Δ = -222-4·2·48
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{-(-22)-10}{2*2}=\frac{12}{4} =3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+10}{2*2}=\frac{32}{4} =8 $

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