2x(x+12)=3x=24-x

Solution for 2x(x+12)=3x=24-x equation:

2x(x+12)=3x=24-x

We move all terms to the left:

2x(x+12)-(3x)=0

We add all the numbers together, and all the variables

-3x+2x(x+12)=0

We multiply parentheses

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

We add all the numbers together, and all the variables

2x^2+21x=0

a = 2; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·2·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*2}=\frac{-42}{4}
=-10+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*2}=\frac{0}{4}
=0
$