x=18x-6x^2+8

Solution for x=18x-6x^2+8 equation:

x=18x-6x^2+8

We move all terms to the left:

x-(18x-6x^2+8)=0

We get rid of parentheses

6x^2-18x+x-8=0

We add all the numbers together, and all the variables

6x^2-17x-8=0

a = 6; b = -17; c = -8;
Δ = b2-4ac
Δ = -172-4·6·(-8)
Δ = 481
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{-(-17)-\sqrt{481}}{2*6}=\frac{17-\sqrt{481}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{481}}{2*6}=\frac{17+\sqrt{481}}{12}
$