x+(3/x)=25

Solution for x+(3/x)=25 equation:

x+(3/x)=25

We move all terms to the left:

x+(3/x)-(25)=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/x)-25=0

We get rid of parentheses

x+3/x-25=0

We multiply all the terms by the denominator


x*x-25*x+3=0

We add all the numbers together, and all the variables

-25x+x*x+3=0

Wy multiply elements

x^2-25x+3=0

a = 1; b = -25; c = +3;
Δ = b2-4ac
Δ = -252-4·1·3
Δ = 613
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{-(-25)-\sqrt{613}}{2*1}=\frac{25-\sqrt{613}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{613}}{2*1}=\frac{25+\sqrt{613}}{2}
$