(216x-4)-(x^2-9)=0

Solution for (216x-4)-(x^2-9)=0 equation:

(216x-4)-(x^2-9)=0

We get rid of parentheses

-x^2+216x-4+9=0

We add all the numbers together, and all the variables

-1x^2+216x+5=0

a = -1; b = 216; c = +5;
Δ = b2-4ac
Δ = 2162-4·(-1)·5
Δ = 46676
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:

$\sqrt{\Delta}=\sqrt{46676}=\sqrt{4*11669}=\sqrt{4}*\sqrt{11669}=2\sqrt{11669}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-2\sqrt{11669}}{2*-1}=\frac{-216-2\sqrt{11669}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+2\sqrt{11669}}{2*-1}=\frac{-216+2\sqrt{11669}}{-2}
$