224=216-18x+x^2

Solution for 224=216-18x+x^2 equation:

224=216-18x+x^2

We move all terms to the left:

224-(216-18x+x^2)=0

We get rid of parentheses

-x^2+18x-216+224=0

We add all the numbers together, and all the variables

-1x^2+18x+8=0

a = -1; b = 18; c = +8;
Δ = b2-4ac
Δ = 182-4·(-1)·8
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{89}}{2*-1}=\frac{-18-2\sqrt{89}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{89}}{2*-1}=\frac{-18+2\sqrt{89}}{-2}
$