(4x)+(4/x)=10

Solution for (4x)+(4/x)=10 equation:

(4x)+(4/x)=10

We move all terms to the left:

(4x)+(4/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

4x+(+4/x)-10=0

We get rid of parentheses

4x+4/x-10=0

We multiply all the terms by the denominator


4x*x-10*x+4=0

We add all the numbers together, and all the variables

-10x+4x*x+4=0

Wy multiply elements

4x^2-10x+4=0

a = 4; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·4·4
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6}{2*4}=\frac{4}{8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6}{2*4}=\frac{16}{8}
=2
$