3x(4-x)=6

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

3x(4-x)=6

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x(-1x+4)-6=0

We multiply parentheses

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

a = -3; b = 12; c = -6;
Δ = b2-4ac
Δ = 122-4·(-3)·(-6)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{2}}{2*-3}=\frac{-12-6\sqrt{2}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{2}}{2*-3}=\frac{-12+6\sqrt{2}}{-6}
$