25=x+3/x

Solution for 25=x+3/x equation:

25=x+3/x

We move all terms to the left:

25-(x+3/x)=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

-1x^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}
$