x^2-x(26/x)=26x

Solution for x^2-x(26/x)=26x equation:

x^2-x(26/x)=26x

We move all terms to the left:

x^2-x(26/x)-(26x)=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^2-x(+26/x)-26x=0

We add all the numbers together, and all the variables

x^2-26x-x(+26/x)=0

We multiply parentheses

x^2-26x^2-26x=0

We add all the numbers together, and all the variables

-25x^2-26x=0

a = -25; b = -26; c = 0;
Δ = b2-4ac
Δ = -262-4·(-25)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-26}{2*-25}=\frac{0}{-50}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+26}{2*-25}=\frac{52}{-50}
=-1+1/25
$