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

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

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

We move all terms to the left:

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


Domain of the equation: 2)(2p+5)!=0

p∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We get rid of parentheses

2p^2+1p*2*5+1=0

Wy multiply elements

2p^2+10p*5+1=0

Wy multiply elements

2p^2+50p+1=0

a = 2; b = 50; c = +1;
Δ = b2-4ac
Δ = 502-4·2·1
Δ = 2492
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:

$\sqrt{\Delta}=\sqrt{2492}=\sqrt{4*623}=\sqrt{4}*\sqrt{623}=2\sqrt{623}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{623}}{2*2}=\frac{-50-2\sqrt{623}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{623}}{2*2}=\frac{-50+2\sqrt{623}}{4}
$