10=11+8/x-x

Solution for 10=11+8/x-x equation:

10=11+8/x-x

We move all terms to the left:

10-(11+8/x-x)=0


Domain of the equation: x-x)!=0

x∈R


We add all the numbers together, and all the variables

-(-1x+8/x+11)+10=0

We get rid of parentheses

1x-8/x-11+10=0

We multiply all the terms by the denominator


1x*x-11*x+10*x-8=0

We add all the numbers together, and all the variables

-1x+1x*x-8=0

Wy multiply elements

x^2-1x-8=0

a = 1; b = -1; c = -8;
Δ = b2-4ac
Δ = -12-4·1·(-8)
Δ = 33
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{-(-1)-\sqrt{33}}{2*1}=\frac{1-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*1}=\frac{1+\sqrt{33}}{2}
$