((-7x^2)+28)/(x^2+4)=0

Solution for ((-7x^2)+28)/(x^2+4)=0 equation:

((-7x^2)+28)/(x^2+4)=0


Domain of the equation: (x^2+4)!=0

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

x^2!=-4

x^2!=-4/

x^2!=√-1/0

x!=NAN

x∈R


We multiply all the terms by the denominator


((-7x^2)+28)=0


We calculate terms in parentheses: +((-7x^2)+28), so:

(-7x^2)+28

We get rid of parentheses

-7x^2+28

Back to the equation:

+(-7x^2+28)


We get rid of parentheses

-7x^2+28=0

a = -7; b = 0; c = +28;
Δ = b2-4ac
Δ = 02-4·(-7)·28
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28}{2*-7}=\frac{-28}{-14}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28}{2*-7}=\frac{28}{-14}
=-2
$