x=(9x-34)(20-x)

Solution for x=(9x-34)(20-x) equation:

x=(9x-34)(20-x)

We move all terms to the left:

x-((9x-34)(20-x))=0

We add all the numbers together, and all the variables

x-((9x-34)(-1x+20))=0

We multiply parentheses ..

-((-9x^2+180x+34x-680))+x=0


We calculate terms in parentheses: -((-9x^2+180x+34x-680)), so:

(-9x^2+180x+34x-680)

We get rid of parentheses

-9x^2+180x+34x-680

We add all the numbers together, and all the variables

-9x^2+214x-680

Back to the equation:

-(-9x^2+214x-680)


We get rid of parentheses

9x^2-214x+x+680=0

We add all the numbers together, and all the variables

9x^2-213x+680=0

a = 9; b = -213; c = +680;
Δ = b2-4ac
Δ = -2132-4·9·680
Δ = 20889
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:

$\sqrt{\Delta}=\sqrt{20889}=\sqrt{9*2321}=\sqrt{9}*\sqrt{2321}=3\sqrt{2321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-213)-3\sqrt{2321}}{2*9}=\frac{213-3\sqrt{2321}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-213)+3\sqrt{2321}}{2*9}=\frac{213+3\sqrt{2321}}{18}
$