12-35p+16^P2+(-8p+9)(-1+2p)=0

Solution for 12-35p+16^P2+(-8p+9)(-1+2p)=0 equation:

12-35p+16^2+(-8p+9)(-1+2p)=0

We add all the numbers together, and all the variables

-35p+(-8p+9)(2p-1)+12+16^2=0

We add all the numbers together, and all the variables

-35p+(-8p+9)(2p-1)+268=0

We multiply parentheses ..

(-16p^2+8p+18p-9)-35p+268=0

We get rid of parentheses

-16p^2+8p+18p-35p-9+268=0

We add all the numbers together, and all the variables

-16p^2-9p+259=0

a = -16; b = -9; c = +259;
Δ = b2-4ac
Δ = -92-4·(-16)·259
Δ = 16657
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{16657}}{2*-16}=\frac{9-\sqrt{16657}}{-32}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{16657}}{2*-16}=\frac{9+\sqrt{16657}}{-32}
$