-8(1+4p)7p=-25-8p

Solution for -8(1+4p)7p=-25-8p equation:

-8(1+4p)7p=-25-8p

We move all terms to the left:

-8(1+4p)7p-(-25-8p)=0

We add all the numbers together, and all the variables

-8(4p+1)7p-(-8p-25)=0

We multiply parentheses

-224p^2-56p-(-8p-25)=0

We get rid of parentheses

-224p^2-56p+8p+25=0

We add all the numbers together, and all the variables

-224p^2-48p+25=0

a = -224; b = -48; c = +25;
Δ = b2-4ac
Δ = -482-4·(-224)·25
Δ = 24704
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:

$\sqrt{\Delta}=\sqrt{24704}=\sqrt{64*386}=\sqrt{64}*\sqrt{386}=8\sqrt{386}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{386}}{2*-224}=\frac{48-8\sqrt{386}}{-448}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{386}}{2*-224}=\frac{48+8\sqrt{386}}{-448}
$