9x*x-x-216=0

Solution for 9x*x-x-216=0 equation:

9x*x-x-216=0

We add all the numbers together, and all the variables

-1x+9x*x-216=0

Wy multiply elements

9x^2-1x-216=0

a = 9; b = -1; c = -216;
Δ = b2-4ac
Δ = -12-4·9·(-216)
Δ = 7777
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{-(-1)-\sqrt{7777}}{2*9}=\frac{1-\sqrt{7777}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{7777}}{2*9}=\frac{1+\sqrt{7777}}{18}
$