(5(x^2-7))/(x^2+7)^2=0

Solution for (5(x^2-7))/(x^2+7)^2=0 equation:

(5(x^2-7))/(x^2+7)^2=0


Domain of the equation: (x^2+7)^2!=0

x∈R


We multiply all the terms by the denominator


(5(x^2-7))=0


We calculate terms in parentheses: +(5(x^2-7)), so:

5(x^2-7)

We multiply parentheses

5x^2-35

Back to the equation:

+(5x^2-35)


We get rid of parentheses

5x^2-35=0

a = 5; b = 0; c = -35;
Δ = b2-4ac
Δ = 02-4·5·(-35)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{7}}{2*5}=\frac{0-10\sqrt{7}}{10}
=-\frac{10\sqrt{7}}{10}
=-\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{7}}{2*5}=\frac{0+10\sqrt{7}}{10}
=\frac{10\sqrt{7}}{10}
=\sqrt{7}
$