3(1+p)+4=p+2.5(2+4p)p=

Solution for 3(1+p)+4=p+2.5(2+4p)p= equation:

3(1+p)+4=p+2.5(2+4p)p=

We move all terms to the left:

3(1+p)+4-(p+2.5(2+4p)p)=0

We add all the numbers together, and all the variables

3(p+1)-(p+2.5(4p+2)p)+4=0

We multiply parentheses

3p-(p+2.5(4p+2)p)+3+4=0


We calculate terms in parentheses: -(p+2.5(4p+2)p), so:

p+2.5(4p+2)p

We multiply parentheses

8p^2+p+4p

We add all the numbers together, and all the variables

8p^2+5p

Back to the equation:

-(8p^2+5p)


We add all the numbers together, and all the variables

3p-(8p^2+5p)+7=0

We get rid of parentheses

-8p^2+3p-5p+7=0

We add all the numbers together, and all the variables

-8p^2-2p+7=0

a = -8; b = -2; c = +7;
Δ = b2-4ac
Δ = -22-4·(-8)·7
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{57}}{2*-8}=\frac{2-2\sqrt{57}}{-16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{57}}{2*-8}=\frac{2+2\sqrt{57}}{-16}
$