x*(16-x)=63

Solution for x*(16-x)=63 equation:

x(16-x)=63

We move all terms to the left:

x(16-x)-(63)=0

We add all the numbers together, and all the variables

x(-1x+16)-63=0

We multiply parentheses

-1x^2+16x-63=0

a = -1; b = 16; c = -63;
Δ = b2-4ac
Δ = 162-4·(-1)·(-63)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2}{2*-1}=\frac{-14}{-2}
=+7
$