2p^2-6p-58=0

Solution for 2p^2-6p-58=0 equation:

2p^2-6p-58=0

a = 2; b = -6; c = -58;
Δ = b2-4ac
Δ = -62-4·2·(-58)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10\sqrt{5}}{2*2}=\frac{6-10\sqrt{5}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10\sqrt{5}}{2*2}=\frac{6+10\sqrt{5}}{4}
$