4p^2-30p+11=0

Solution for 4p^2-30p+11=0 equation:

4p^2-30p+11=0

a = 4; b = -30; c = +11;
Δ = b2-4ac
Δ = -302-4·4·11
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{181}}{2*4}=\frac{30-2\sqrt{181}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{181}}{2*4}=\frac{30+2\sqrt{181}}{8}
$