4p^2-5p-1=4p

Solution for 4p^2-5p-1=4p equation:

4p^2-5p-1=4p

We move all terms to the left:

4p^2-5p-1-(4p)=0

We add all the numbers together, and all the variables

4p^2-9p-1=0

a = 4; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·4·(-1)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{97}}{2*4}=\frac{9-\sqrt{97}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{97}}{2*4}=\frac{9+\sqrt{97}}{8}
$