6x(x+3)=6x+18

Solution for 6x(x+3)=6x+18 equation:

6x(x+3)=6x+18

We move all terms to the left:

6x(x+3)-(6x+18)=0

We multiply parentheses

6x^2+18x-(6x+18)=0

We get rid of parentheses

6x^2+18x-6x-18=0

We add all the numbers together, and all the variables

6x^2+12x-18=0

a = 6; b = 12; c = -18;
Δ = b2-4ac
Δ = 122-4·6·(-18)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*6}=\frac{12}{12}
=1
$