X=11/x+10

Solution for X=11/x+10 equation:

X=11/X+10

We move all terms to the left:

X-(11/X+10)=0


Domain of the equation: X+10)!=0

X∈R


We get rid of parentheses

X-11/X-10=0

We multiply all the terms by the denominator


X*X-10*X-11=0

We add all the numbers together, and all the variables

-10X+X*X-11=0

Wy multiply elements

X^2-10X-11=0

a = 1; b = -10; c = -11;
Δ = b2-4ac
Δ = -102-4·1·(-11)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-12}{2*1}=\frac{-2}{2}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+12}{2*1}=\frac{22}{2}
=11
$