2x(x-8)=24x^2

Solution for 2x(x-8)=24x^2 equation:

2x(x-8)=24x^2

We move all terms to the left:

2x(x-8)-(24x^2)=0

determiningTheFunctionDomain
-24x^2+2x(x-8)=0

We multiply parentheses

-24x^2+2x^2-16x=0

We add all the numbers together, and all the variables

-22x^2-16x=0

a = -22; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-22)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-22}=\frac{0}{-44}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-22}=\frac{32}{-44}
=-8/11
$