x+(3.84/x)=10

Solution for x+(3.84/x)=10 equation:

x+(3.84/x)=10

We move all terms to the left:

x+(3.84/x)-(10)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(+3.84/x)-10=0

We get rid of parentheses

x+3.84/x-10=0

We multiply all the terms by the denominator


x*x-10*x+3.84=0

We add all the numbers together, and all the variables

-10x+x*x+3.84=0

Wy multiply elements

x^2-10x+3.84=0

a = 1; b = -10; c = +3.84;
Δ = b2-4ac
Δ = -102-4·1·3.84
Δ = 84.64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-\sqrt{84.64}}{2*1}=\frac{10-\sqrt{84.64}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+\sqrt{84.64}}{2*1}=\frac{10+\sqrt{84.64}}{2}
$