(x^2-9)/(5+x^2)=-5/9

Solution for (x^2-9)/(5+x^2)=-5/9 equation:

(x^2-9)/(5+x^2)=-5/9

We move all terms to the left:

(x^2-9)/(5+x^2)-(-5/9)=0


Domain of the equation: (5+x^2)!=0

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

x^2!=-5

x^2!=-5/

x^2!=√-1/0

x!=NAN

x∈R


We get rid of parentheses

(x^2-9)/(5+x^2)+5/9=0

We calculate fractions


(9x^2-81)/(9x^2+45)+(5x^2+25)/(9x^2+45)=0

We multiply all the terms by the denominator


(9x^2-81)+(5x^2+25)=0

We get rid of parentheses

9x^2+5x^2-81+25=0

We add all the numbers together, and all the variables

14x^2-56=0

a = 14; b = 0; c = -56;
Δ = b2-4ac
Δ = 02-4·14·(-56)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-56}{2*14}=\frac{-56}{28}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+56}{2*14}=\frac{56}{28}
=2
$