3x(12-x)=24-x

Solution for 3x(12-x)=24-x equation:

3x(12-x)=24-x

We move all terms to the left:

3x(12-x)-(24-x)=0

We add all the numbers together, and all the variables

3x(-1x+12)-(-1x+24)=0

We multiply parentheses

-3x^2+36x-(-1x+24)=0

We get rid of parentheses

-3x^2+36x+1x-24=0

We add all the numbers together, and all the variables

-3x^2+37x-24=0

a = -3; b = 37; c = -24;
Δ = b2-4ac
Δ = 372-4·(-3)·(-24)
Δ = 1081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-\sqrt{1081}}{2*-3}=\frac{-37-\sqrt{1081}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{1081}}{2*-3}=\frac{-37+\sqrt{1081}}{-6}
$