16-x^2/(x^2+6x-40)=0

Solution for 16-x^2/(x^2+6x-40)=0 equation:

16-x^2/(x^2+6x-40)=0


Domain of the equation: (x^2+6x-40)!=0

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

x^2+6x!=40

x∈R


We multiply all the terms by the denominator


-x^2+16*(x^2+6x-40)=0

We add all the numbers together, and all the variables

-1x^2+16*(x^2+6x-40)=0

We multiply parentheses

-1x^2+16x^2+96x-640=0

We add all the numbers together, and all the variables

15x^2+96x-640=0

a = 15; b = 96; c = -640;
Δ = b2-4ac
Δ = 962-4·15·(-640)
Δ = 47616
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:

$\sqrt{\Delta}=\sqrt{47616}=\sqrt{256*186}=\sqrt{256}*\sqrt{186}=16\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-16\sqrt{186}}{2*15}=\frac{-96-16\sqrt{186}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+16\sqrt{186}}{2*15}=\frac{-96+16\sqrt{186}}{30}
$