36x-x^2-180=0

Solution for 36x-x^2-180=0 equation:

36x-x^2-180=0

We add all the numbers together, and all the variables

-1x^2+36x-180=0

a = -1; b = 36; c = -180;
Δ = b2-4ac
Δ = 362-4·(-1)·(-180)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-24}{2*-1}=\frac{-60}{-2}
=+30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+24}{2*-1}=\frac{-12}{-2}
=+6
$