5p^2-58p+21=0

Solution for 5p^2-58p+21=0 equation:

5p^2-58p+21=0

a = 5; b = -58; c = +21;
Δ = b2-4ac
Δ = -582-4·5·21
Δ = 2944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-8\sqrt{46}}{2*5}=\frac{58-8\sqrt{46}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+8\sqrt{46}}{2*5}=\frac{58+8\sqrt{46}}{10}
$