2(6p)=2(1/2)(4p+8)

Solution for 2(6p)=2(1/2)(4p+8) equation:

2(6p)=2(1/2)(4p+8)

We move all terms to the left:

2(6p)-(2(1/2)(4p+8))=0


Domain of the equation: 2)(4p+8))!=0

p∈R


We add all the numbers together, and all the variables

26p-(2(+1/2)(4p+8))=0

We multiply parentheses ..

-(2(+4p^2+1/2*8))+26p=0

We multiply all the terms by the denominator


-(2(+4p^2+1+26p*2*8))=0


We calculate terms in parentheses: -(2(+4p^2+1+26p*2*8)), so:

2(+4p^2+1+26p*2*8)

We multiply parentheses

8p^2+832p+2

Back to the equation:

-(8p^2+832p+2)


We get rid of parentheses

-8p^2-832p-2=0

a = -8; b = -832; c = -2;
Δ = b2-4ac
Δ = -8322-4·(-8)·(-2)
Δ = 692160
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:

$\sqrt{\Delta}=\sqrt{692160}=\sqrt{64*10815}=\sqrt{64}*\sqrt{10815}=8\sqrt{10815}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-832)-8\sqrt{10815}}{2*-8}=\frac{832-8\sqrt{10815}}{-16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-832)+8\sqrt{10815}}{2*-8}=\frac{832+8\sqrt{10815}}{-16}
$