(1/2)*(2p+9)=-p+5

Solution for (1/2)*(2p+9)=-p+5 equation:

(1/2)(2p+9)=-p+5

We move all terms to the left:

(1/2)(2p+9)-(-p+5)=0


Domain of the equation: 2)(2p+9)!=0

p∈R


We add all the numbers together, and all the variables

(+1/2)(2p+9)-(-1p+5)=0

We get rid of parentheses

(+1/2)(2p+9)+1p-5=0

We multiply parentheses ..

(+2p^2+1/2*9)+1p-5=0

We multiply all the terms by the denominator


(+2p^2+1+1p*2*9)-5*2*9)=0

We add all the numbers together, and all the variables

(+2p^2+1+1p*2*9)=0

We get rid of parentheses

2p^2+1p*2*9+1=0

Wy multiply elements

2p^2+18p*9+1=0

Wy multiply elements

2p^2+162p+1=0

a = 2; b = 162; c = +1;
Δ = b2-4ac
Δ = 1622-4·2·1
Δ = 26236
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:

$\sqrt{\Delta}=\sqrt{26236}=\sqrt{4*6559}=\sqrt{4}*\sqrt{6559}=2\sqrt{6559}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-2\sqrt{6559}}{2*2}=\frac{-162-2\sqrt{6559}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+2\sqrt{6559}}{2*2}=\frac{-162+2\sqrt{6559}}{4}
$