(4x+8)(9x-27)=x

Solution for (4x+8)(9x-27)=x equation:

(4x+8)(9x-27)=x

We move all terms to the left:

(4x+8)(9x-27)-(x)=0

We add all the numbers together, and all the variables

-1x+(4x+8)(9x-27)=0

We multiply parentheses ..

(+36x^2-108x+72x-216)-1x=0

We get rid of parentheses

36x^2-108x+72x-1x-216=0

We add all the numbers together, and all the variables

36x^2-37x-216=0

a = 36; b = -37; c = -216;
Δ = b2-4ac
Δ = -372-4·36·(-216)
Δ = 32473
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{-(-37)-\sqrt{32473}}{2*36}=\frac{37-\sqrt{32473}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{32473}}{2*36}=\frac{37+\sqrt{32473}}{72}
$