6x-x^2=-72

Solution for 6x-x^2=-72 equation:

6x-x^2=-72

We move all terms to the left:

6x-x^2-(-72)=0

We add all the numbers together, and all the variables

-1x^2+6x+72=0

a = -1; b = 6; c = +72;
Δ = b2-4ac
Δ = 62-4·(-1)·72
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{-(6)-18}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*-1}=\frac{12}{-2}
=-6
$