((x^2)+7x+4)/(x+6)=0

Solution for ((x^2)+7x+4)/(x+6)=0 equation:

((x^2)+7x+4)/(x+6)=0


Domain of the equation: (x+6)!=0

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

x!=-6

x∈R


We multiply all the terms by the denominator


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

We get rid of parentheses

x^2+7x+4=0

a = 1; b = 7; c = +4;
Δ = b2-4ac
Δ = 72-4·1·4
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{33}}{2*1}=\frac{-7-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{33}}{2*1}=\frac{-7+\sqrt{33}}{2}
$