5r^2-58r+80=0

Solution for 5r^2-58r+80=0 equation:

5r^2-58r+80=0

a = 5; b = -58; c = +80;
Δ = b2-4ac
Δ = -582-4·5·80
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-42}{2*5}=\frac{16}{10}
=1+3/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+42}{2*5}=\frac{100}{10}
=10
$