0=x^2-24x+80

Solution for 0=x^2-24x+80 equation:

0=x^2-24x+80

We move all terms to the left:

0-(x^2-24x+80)=0

We add all the numbers together, and all the variables

-(x^2-24x+80)=0

We get rid of parentheses

-x^2+24x-80=0

We add all the numbers together, and all the variables

-1x^2+24x-80=0

a = -1; b = 24; c = -80;
Δ = b2-4ac
Δ = 242-4·(-1)·(-80)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16}{2*-1}=\frac{-40}{-2}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16}{2*-1}=\frac{-8}{-2}
=+4
$