-x-1/x(x)-25=9x

Solution for -x-1/x(x)-25=9x equation:

-x-1/x(x)-25=9x

We move all terms to the left:

-x-1/x(x)-25-(9x)=0


Domain of the equation: xx!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-10x-1/xx-25=0

We multiply all the terms by the denominator


-10x*xx-25*xx-1=0

Wy multiply elements

-10x^2-25x-1=0

a = -10; b = -25; c = -1;
Δ = b2-4ac
Δ = -252-4·(-10)·(-1)
Δ = 585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-3\sqrt{65}}{2*-10}=\frac{25-3\sqrt{65}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+3\sqrt{65}}{2*-10}=\frac{25+3\sqrt{65}}{-20}
$