-24=4x(x-4)-6x

Solution for -24=4x(x-4)-6x equation:

-24=4x(x-4)-6x

We move all terms to the left:

-24-(4x(x-4)-6x)=0


We calculate terms in parentheses: -(4x(x-4)-6x), so:

4x(x-4)-6x

We add all the numbers together, and all the variables

-6x+4x(x-4)

We multiply parentheses

4x^2-6x-16x

We add all the numbers together, and all the variables

4x^2-22x

Back to the equation:

-(4x^2-22x)


We get rid of parentheses

-4x^2+22x-24=0

a = -4; b = 22; c = -24;
Δ = b2-4ac
Δ = 222-4·(-4)·(-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{-(22)-10}{2*-4}=\frac{-32}{-8}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+10}{2*-4}=\frac{-12}{-8}
=1+1/2
$