x+(.82/x)=4

Solution for x+(.82/x)=4 equation:

x+(.82/x)=4

We move all terms to the left:

x+(.82/x)-(4)=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+(+.82/x)-4=0

We get rid of parentheses

x+.82/x-4=0

We multiply all the terms by the denominator


x*x-4*x+.82=0

We add all the numbers together, and all the variables

-4x+x*x+0.82=0

Wy multiply elements

x^2-4x+0.82=0

a = 1; b = -4; c = +0.82;
Δ = b2-4ac
Δ = -42-4·1·0.82
Δ = 12.72
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{-(-4)-\sqrt{12.72}}{2*1}=\frac{4-\sqrt{12.72}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{12.72}}{2*1}=\frac{4+\sqrt{12.72}}{2}
$