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

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

(-2(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


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


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

-2(x^2-7)

We multiply parentheses

-2x^2+14

Back to the equation:

+(-2x^2+14)


We get rid of parentheses

-2x^2+14=0

a = -2; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-2)·14
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*-2}=\frac{0-4\sqrt{7}}{-4}
=-\frac{4\sqrt{7}}{-4}
=-\frac{\sqrt{7}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*-2}=\frac{0+4\sqrt{7}}{-4}
=\frac{4\sqrt{7}}{-4}
=\frac{\sqrt{7}}{-1}
$