3x(4x-24)=x

Solution for 3x(4x-24)=x equation:

3x(4x-24)=x

We move all terms to the left:

3x(4x-24)-(x)=0

We add all the numbers together, and all the variables

-1x+3x(4x-24)=0

We multiply parentheses

12x^2-1x-72x=0

We add all the numbers together, and all the variables

12x^2-73x=0

a = 12; b = -73; c = 0;
Δ = b2-4ac
Δ = -732-4·12·0
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-73)-73}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-73)+73}{2*12}=\frac{146}{24}
=6+1/12
$