-x2+12x=16

Solution for -x2+12x=16 equation:

-x2+12x=16

We move all terms to the left:

-x2+12x-(16)=0

We add all the numbers together, and all the variables

-1x^2+12x-16=0

a = -1; b = 12; c = -16;
Δ = b2-4ac
Δ = 122-4·(-1)·(-16)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{5}}{2*-1}=\frac{-12-4\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{5}}{2*-1}=\frac{-12+4\sqrt{5}}{-2}
$