-8p(4p-12)+36-3=-127

Solution for -8p(4p-12)+36-3=-127 equation:

-8p(4p-12)+36-3=-127

We move all terms to the left:

-8p(4p-12)+36-3-(-127)=0

We add all the numbers together, and all the variables

-8p(4p-12)+160=0

We multiply parentheses

-32p^2+96p+160=0

a = -32; b = 96; c = +160;
Δ = b2-4ac
Δ = 962-4·(-32)·160
Δ = 29696
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:

$\sqrt{\Delta}=\sqrt{29696}=\sqrt{1024*29}=\sqrt{1024}*\sqrt{29}=32\sqrt{29}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-32\sqrt{29}}{2*-32}=\frac{-96-32\sqrt{29}}{-64}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+32\sqrt{29}}{2*-32}=\frac{-96+32\sqrt{29}}{-64}
$