10+11/x=-40+x

Solution for 10+11/x=-40+x equation:

10+11/x=-40+x

We move all terms to the left:

10+11/x-(-40+x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

11/x-(x-40)+10=0

We get rid of parentheses

11/x-x+40+10=0

We multiply all the terms by the denominator


-x*x+40*x+10*x+11=0

We add all the numbers together, and all the variables

50x-x*x+11=0

Wy multiply elements

-1x^2+50x+11=0

a = -1; b = 50; c = +11;
Δ = b2-4ac
Δ = 502-4·(-1)·11
Δ = 2544
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:

$\sqrt{\Delta}=\sqrt{2544}=\sqrt{16*159}=\sqrt{16}*\sqrt{159}=4\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-4\sqrt{159}}{2*-1}=\frac{-50-4\sqrt{159}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+4\sqrt{159}}{2*-1}=\frac{-50+4\sqrt{159}}{-2}
$