5p^2-22p-1=4+2p

Solution for 5p^2-22p-1=4+2p equation:

5p^2-22p-1=4+2p

We move all terms to the left:

5p^2-22p-1-(4+2p)=0

We add all the numbers together, and all the variables

5p^2-22p-(2p+4)-1=0

We get rid of parentheses

5p^2-22p-2p-4-1=0

We add all the numbers together, and all the variables

5p^2-24p-5=0

a = 5; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·5·(-5)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-26}{2*5}=\frac{-2}{10}
=-1/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+26}{2*5}=\frac{50}{10}
=5
$