4p^2-p-32=0

Solution for 4p^2-p-32=0 equation:

4p^2-p-32=0

We add all the numbers together, and all the variables

4p^2-1p-32=0

a = 4; b = -1; c = -32;
Δ = b2-4ac
Δ = -12-4·4·(-32)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{57}}{2*4}=\frac{1-3\sqrt{57}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{57}}{2*4}=\frac{1+3\sqrt{57}}{8}
$