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

Solution for 24(x-1)+x(x-1)(4)=24x equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

4x^2-24x+24x-4x-24=0

We add all the numbers together, and all the variables

4x^2-4x-24=0

a = 4; b = -4; c = -24;
Δ = b2-4ac
Δ = -42-4·4·(-24)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-20}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+20}{2*4}=\frac{24}{8}
=3
$