3x(x-4)+6=9

Solution for 3x(x-4)+6=9 equation:

3x(x-4)+6=9

We move all terms to the left:

3x(x-4)+6-(9)=0

We add all the numbers together, and all the variables

3x(x-4)-3=0

We multiply parentheses

3x^2-12x-3=0

a = 3; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·3·(-3)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{5}}{2*3}=\frac{12-6\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{5}}{2*3}=\frac{12+6\sqrt{5}}{6}
$