5=-x^2+6x+19

Solution for 5=-x^2+6x+19 equation:

5=-x^2+6x+19

We move all terms to the left:

5-(-x^2+6x+19)=0

We get rid of parentheses

x^2-6x-19+5=0

We add all the numbers together, and all the variables

x^2-6x-14=0

a = 1; b = -6; c = -14;
Δ = b2-4ac
Δ = -62-4·1·(-14)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{23}}{2*1}=\frac{6-2\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{23}}{2*1}=\frac{6+2\sqrt{23}}{2}
$