24(2x-1)=8x(2x-2)+2x

Solution for 24(2x-1)=8x(2x-2)+2x equation:

24(2x-1)=8x(2x-2)+2x

We move all terms to the left:

24(2x-1)-(8x(2x-2)+2x)=0

We multiply parentheses

48x-(8x(2x-2)+2x)-24=0


We calculate terms in parentheses: -(8x(2x-2)+2x), so:

8x(2x-2)+2x

We add all the numbers together, and all the variables

2x+8x(2x-2)

We multiply parentheses

16x^2+2x-16x

We add all the numbers together, and all the variables

16x^2-14x

Back to the equation:

-(16x^2-14x)


We get rid of parentheses

-16x^2+48x+14x-24=0

We add all the numbers together, and all the variables

-16x^2+62x-24=0

a = -16; b = 62; c = -24;
Δ = b2-4ac
Δ = 622-4·(-16)·(-24)
Δ = 2308
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:

$\sqrt{\Delta}=\sqrt{2308}=\sqrt{4*577}=\sqrt{4}*\sqrt{577}=2\sqrt{577}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{577}}{2*-16}=\frac{-62-2\sqrt{577}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{577}}{2*-16}=\frac{-62+2\sqrt{577}}{-32}
$