-x^2+22x-60.5=0

Solution for -x^2+22x-60.5=0 equation:

-x^2+22x-60.5=0

We add all the numbers together, and all the variables

-1x^2+22x-60.5=0

a = -1; b = 22; c = -60.5;
Δ = b2-4ac
Δ = 222-4·(-1)·(-60.5)
Δ = 242
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:

$\sqrt{\Delta}=\sqrt{242}=\sqrt{121*2}=\sqrt{121}*\sqrt{2}=11\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-11\sqrt{2}}{2*-1}=\frac{-22-11\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+11\sqrt{2}}{2*-1}=\frac{-22+11\sqrt{2}}{-2}
$