(2p-3)(p+1)-p(2)=51

Solution for (2p-3)(p+1)-p(2)=51 equation:

(2p-3)(p+1)-p(2)=51

We move all terms to the left:

(2p-3)(p+1)-p(2)-(51)=0

We add all the numbers together, and all the variables

-1p^2+(2p-3)(p+1)-51=0

We multiply parentheses ..

-1p^2+(+2p^2+2p-3p-3)-51=0

We get rid of parentheses

-1p^2+2p^2+2p-3p-3-51=0

We add all the numbers together, and all the variables

p^2-1p-54=0

a = 1; b = -1; c = -54;
Δ = b2-4ac
Δ = -12-4·1·(-54)
Δ = 217
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{-(-1)-\sqrt{217}}{2*1}=\frac{1-\sqrt{217}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{217}}{2*1}=\frac{1+\sqrt{217}}{2}
$