x+5-(9/x+5)=10

Solution for x+5-(9/x+5)=10 equation:

x+5-(9/x+5)=10

We move all terms to the left:

x+5-(9/x+5)-(10)=0


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

x∈R


We add all the numbers together, and all the variables

x-(9/x+5)-5=0

We get rid of parentheses

x-9/x-5-5=0

We multiply all the terms by the denominator


x*x-5*x-5*x-9=0

We add all the numbers together, and all the variables

-10x+x*x-9=0

Wy multiply elements

x^2-10x-9=0

a = 1; b = -10; c = -9;
Δ = b2-4ac
Δ = -102-4·1·(-9)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{34}}{2*1}=\frac{10-2\sqrt{34}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{34}}{2*1}=\frac{10+2\sqrt{34}}{2}
$