30x-x^2=144

Solution for 30x-x^2=144 equation:

30x-x^2=144

We move all terms to the left:

30x-x^2-(144)=0

We add all the numbers together, and all the variables

-1x^2+30x-144=0

a = -1; b = 30; c = -144;
Δ = b2-4ac
Δ = 302-4·(-1)·(-144)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-18}{2*-1}=\frac{-48}{-2}
=+24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18}{2*-1}=\frac{-12}{-2}
=+6
$