48/x+2x=22

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∈R


We add all the numbers together, and all the variables

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
$