9(2-3x)29=8x(x-23)

Solution for 9(2-3x)29=8x(x-23) equation:

9(2-3x)29=8x(x-23)

We move all terms to the left:

9(2-3x)29-(8x(x-23))=0

We add all the numbers together, and all the variables

9(-3x+2)29-(8x(x-23))=0

We multiply parentheses

-783x-(8x(x-23))+522=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 get rid of parentheses

-8x^2-783x+184x+522=0

We add all the numbers together, and all the variables

-8x^2-599x+522=0

a = -8; b = -599; c = +522;
Δ = b2-4ac
Δ = -5992-4·(-8)·522
Δ = 375505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-599)-\sqrt{375505}}{2*-8}=\frac{599-\sqrt{375505}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-599)+\sqrt{375505}}{2*-8}=\frac{599+\sqrt{375505}}{-16}
$