3x(4-x)=-3

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

3x(4-x)=-3

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

3x(-1x+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}
$