2p^2-4p-34=0

Solution for 2p^2-4p-34=0 equation:

2p^2-4p-34=0

a = 2; b = -4; c = -34;
Δ = b2-4ac
Δ = -42-4·2·(-34)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12\sqrt{2}}{2*2}=\frac{4-12\sqrt{2}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12\sqrt{2}}{2*2}=\frac{4+12\sqrt{2}}{4}
$