8p^2-6p-1=17

Solution for 8p^2-6p-1=17 equation:

8p^2-6p-1=17

We move all terms to the left:

8p^2-6p-1-(17)=0

We add all the numbers together, and all the variables

8p^2-6p-18=0

a = 8; b = -6; c = -18;
Δ = b2-4ac
Δ = -62-4·8·(-18)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{17}}{2*8}=\frac{6-6\sqrt{17}}{16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{17}}{2*8}=\frac{6+6\sqrt{17}}{16}
$