18=5p+2(p*p)

Solution for 18=5p+2(p*p) equation:

18=5p+2(p*p)

We move all terms to the left:

18-(5p+2(p*p))=0

We add all the numbers together, and all the variables

-(5p+2(+p*p))+18=0


We calculate terms in parentheses: -(5p+2(+p*p)), so:

5p+2(+p*p)

We multiply parentheses

2p^2+5p

Back to the equation:

-(2p^2+5p)


We get rid of parentheses

-2p^2-5p+18=0

a = -2; b = -5; c = +18;
Δ = b2-4ac
Δ = -52-4·(-2)·18
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*-2}=\frac{-8}{-4}
=+2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*-2}=\frac{18}{-4}
=-4+1/2
$