3p^2-30p+1=0

Solution for 3p^2-30p+1=0 equation:

3p^2-30p+1=0

a = 3; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·3·1
Δ = 888
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:

$\sqrt{\Delta}=\sqrt{888}=\sqrt{4*222}=\sqrt{4}*\sqrt{222}=2\sqrt{222}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{222}}{2*3}=\frac{30-2\sqrt{222}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{222}}{2*3}=\frac{30+2\sqrt{222}}{6}
$