5400-36x-x^2=0

Solution for 5400-36x-x^2=0 equation:

5400-36x-x^2=0

We add all the numbers together, and all the variables

-1x^2-36x+5400=0

a = -1; b = -36; c = +5400;
Δ = b2-4ac
Δ = -362-4·(-1)·5400
Δ = 22896
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:

$\sqrt{\Delta}=\sqrt{22896}=\sqrt{144*159}=\sqrt{144}*\sqrt{159}=12\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{159}}{2*-1}=\frac{36-12\sqrt{159}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{159}}{2*-1}=\frac{36+12\sqrt{159}}{-2}
$