4x(x-1)-24=3x(x-2)

Solution for 4x(x-1)-24=3x(x-2) equation:

4x(x-1)-24=3x(x-2)

We move all terms to the left:

4x(x-1)-24-(3x(x-2))=0

We multiply parentheses

4x^2-4x-(3x(x-2))-24=0


We calculate terms in parentheses: -(3x(x-2)), so:

3x(x-2)

We multiply parentheses

3x^2-6x

Back to the equation:

-(3x^2-6x)


We get rid of parentheses

4x^2-3x^2-4x+6x-24=0

We add all the numbers together, and all the variables

x^2+2x-24=0

a = 1; b = 2; c = -24;
Δ = b2-4ac
Δ = 22-4·1·(-24)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*1}=\frac{8}{2}
=4
$