3x(6-3x)=4

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

3x(6-3x)=4

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-9x^2+18x-4=0

a = -9; b = 18; c = -4;
Δ = b2-4ac
Δ = 182-4·(-9)·(-4)
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{-(18)-6\sqrt{5}}{2*-9}=\frac{-18-6\sqrt{5}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{5}}{2*-9}=\frac{-18+6\sqrt{5}}{-18}
$