0=-x^2+16x-61

Solution for 0=-x^2+16x-61 equation:

0=-x^2+16x-61

We move all terms to the left:

0-(-x^2+16x-61)=0

We add all the numbers together, and all the variables

-(-x^2+16x-61)=0

We get rid of parentheses

x^2-16x+61=0

a = 1; b = -16; c = +61;
Δ = b2-4ac
Δ = -162-4·1·61
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{3}}{2*1}=\frac{16-2\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{3}}{2*1}=\frac{16+2\sqrt{3}}{2}
$