4p^2-5p=1

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

4p^2-5p=1

We move all terms to the left:

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

a = 4; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·4·(-1)
Δ = 41
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{-(-5)-\sqrt{41}}{2*4}=\frac{5-\sqrt{41}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{41}}{2*4}=\frac{5+\sqrt{41}}{8}
$