r2-21r+80=0

Solution for r2-21r+80=0 equation:

r2-21r+80=0

We add all the numbers together, and all the variables

r^2-21r+80=0

a = 1; b = -21; c = +80;
Δ = b2-4ac
Δ = -212-4·1·80
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-11}{2*1}=\frac{10}{2}
=5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+11}{2*1}=\frac{32}{2}
=16
$