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

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

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

We move all terms to the left:

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


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

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

x!=-4

x∈R


We multiply all the terms by the denominator


(x^2-2)-7*(x+4)=0

We multiply parentheses

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

We get rid of parentheses

x^2-7x-2-28=0

We add all the numbers together, and all the variables

x^2-7x-30=0

a = 1; b = -7; c = -30;
Δ = b2-4ac
Δ = -72-4·1·(-30)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*1}=\frac{20}{2}
=10
$