2(8x-1)-29=8x(x-23)

Solution for 2(8x-1)-29=8x(x-23) equation:

2(8x-1)-29=8x(x-23)

We move all terms to the left:

2(8x-1)-29-(8x(x-23))=0

We multiply parentheses

16x-(8x(x-23))-2-29=0


We calculate terms in parentheses: -(8x(x-23)), so:

8x(x-23)

We multiply parentheses

8x^2-184x

Back to the equation:

-(8x^2-184x)


We add all the numbers together, and all the variables

16x-(8x^2-184x)-31=0

We get rid of parentheses

-8x^2+16x+184x-31=0

We add all the numbers together, and all the variables

-8x^2+200x-31=0

a = -8; b = 200; c = -31;
Δ = b2-4ac
Δ = 2002-4·(-8)·(-31)
Δ = 39008
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:

$\sqrt{\Delta}=\sqrt{39008}=\sqrt{16*2438}=\sqrt{16}*\sqrt{2438}=4\sqrt{2438}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-4\sqrt{2438}}{2*-8}=\frac{-200-4\sqrt{2438}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+4\sqrt{2438}}{2*-8}=\frac{-200+4\sqrt{2438}}{-16}
$