p^2-30p+91=0

Solution for p^2-30p+91=0 equation:

p^2-30p+91=0

a = 1; b = -30; c = +91;
Δ = b2-4ac
Δ = -302-4·1·91
Δ = 536
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:

$\sqrt{\Delta}=\sqrt{536}=\sqrt{4*134}=\sqrt{4}*\sqrt{134}=2\sqrt{134}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{134}}{2*1}=\frac{30-2\sqrt{134}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{134}}{2*1}=\frac{30+2\sqrt{134}}{2}
$