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

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

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


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

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

2x!=4

x!=4/2

x!=2

x∈R


We multiply all the terms by the denominator


(x^2+6x)=0

We get rid of parentheses

x^2+6x=0

a = 1; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·1·0
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{-(6)-6}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*1}=\frac{0}{2}
=0
$