(4x^2+18x+18)/(2x+6)=0

Solution for (4x^2+18x+18)/(2x+6)=0 equation:

(4x^2+18x+18)/(2x+6)=0


Domain of the equation: (2x+6)!=0

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

2x!=-6

x!=-6/2

x!=-3

x∈R


We multiply all the terms by the denominator


(4x^2+18x+18)=0

We get rid of parentheses

4x^2+18x+18=0

a = 4; b = 18; c = +18;
Δ = b2-4ac
Δ = 182-4·4·18
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6}{2*4}=\frac{-12}{8}
=-1+1/2
$