6x(x+2)-3(x+3)=3

Solution for 6x(x+2)-3(x+3)=3 equation:

6x(x+2)-3(x+3)=3

We move all terms to the left:

6x(x+2)-3(x+3)-(3)=0

We multiply parentheses

6x^2+12x-3x-9-3=0

We add all the numbers together, and all the variables

6x^2+9x-12=0

a = 6; b = 9; c = -12;
Δ = b2-4ac
Δ = 92-4·6·(-12)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{41}}{2*6}=\frac{-9-3\sqrt{41}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{41}}{2*6}=\frac{-9+3\sqrt{41}}{12}
$