-x^2+19x-80=0

Solution for -x^2+19x-80=0 equation:

-x^2+19x-80=0

We add all the numbers together, and all the variables

-1x^2+19x-80=0

a = -1; b = 19; c = -80;
Δ = b2-4ac
Δ = 192-4·(-1)·(-80)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{41}}{2*-1}=\frac{-19-\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{41}}{2*-1}=\frac{-19+\sqrt{41}}{-2}
$