(x-5)+x^2/(x+5)=11

Solution for (x-5)+x^2/(x+5)=11 equation:

(x-5)+x^2/(x+5)=11

We move all terms to the left:

(x-5)+x^2/(x+5)-(11)=0


Domain of the equation: (x+5)!=0

We move all terms containing x to the left, all other terms to the right

x!=-5

x∈R


We get rid of parentheses

x^2/(x+5)+x-5-11=0

We multiply all the terms by the denominator


x^2+x*(x+5)-5*(x+5)-11*(x+5)=0

We multiply parentheses

x^2+x^2+5x-5x-11x-25-55=0

We add all the numbers together, and all the variables

2x^2-11x-80=0

a = 2; b = -11; c = -80;
Δ = b2-4ac
Δ = -112-4·2·(-80)
Δ = 761
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{-(-11)-\sqrt{761}}{2*2}=\frac{11-\sqrt{761}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{761}}{2*2}=\frac{11+\sqrt{761}}{4}
$