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

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

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


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

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

x!=-2

x∈R


We multiply all the terms by the denominator


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

We get rid of parentheses

x^2+4x-2=0

a = 1; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·1·(-2)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{6}}{2*1}=\frac{-4-2\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{6}}{2*1}=\frac{-4+2\sqrt{6}}{2}
$