8x(3x-2)=24x-2

Solution for 8x(3x-2)=24x-2 equation:

8x(3x-2)=24x-2

We move all terms to the left:

8x(3x-2)-(24x-2)=0

We multiply parentheses

24x^2-16x-(24x-2)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

24x^2-40x+2=0

a = 24; b = -40; c = +2;
Δ = b2-4ac
Δ = -402-4·24·2
Δ = 1408
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{22}}{2*24}=\frac{40-8\sqrt{22}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{22}}{2*24}=\frac{40+8\sqrt{22}}{48}
$