40x-x^2-144=0

Solution for 40x-x^2-144=0 equation:

40x-x^2-144=0

We add all the numbers together, and all the variables

-1x^2+40x-144=0

a = -1; b = 40; c = -144;
Δ = b2-4ac
Δ = 402-4·(-1)·(-144)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-32}{2*-1}=\frac{-72}{-2}
=+36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+32}{2*-1}=\frac{-8}{-2}
=+4
$