(2p*p-18p+36)=1

Solution for (2p*p-18p+36)=1 equation:

(2p*p-18p+36)=1

We move all terms to the left:

(2p*p-18p+36)-(1)=0

We add all the numbers together, and all the variables

(-18p+2p*p+36)-1=0

We get rid of parentheses

-18p+2p*p+36-1=0

We add all the numbers together, and all the variables

-18p+2p*p+35=0

Wy multiply elements

2p^2-18p+35=0

a = 2; b = -18; c = +35;
Δ = b2-4ac
Δ = -182-4·2·35
Δ = 44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{11}}{2*2}=\frac{18-2\sqrt{11}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{11}}{2*2}=\frac{18+2\sqrt{11}}{4}
$