30x-x^2=216

Solution for 30x-x^2=216 equation:

30x-x^2=216

We move all terms to the left:

30x-x^2-(216)=0

We add all the numbers together, and all the variables

-1x^2+30x-216=0

a = -1; b = 30; c = -216;
Δ = b2-4ac
Δ = 302-4·(-1)·(-216)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6}{2*-1}=\frac{-36}{-2}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6}{2*-1}=\frac{-24}{-2}
=+12
$