8p+1/2p=9-1/2p

Solution for 8p+1/2p=9-1/2p equation:

8p+1/2p=9-1/2p

We move all terms to the left:

8p+1/2p-(9-1/2p)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 2p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

8p+1/2p-(-1/2p+9)=0

We get rid of parentheses

8p+1/2p+1/2p-9=0

We multiply all the terms by the denominator


8p*2p-9*2p+1+1=0

We add all the numbers together, and all the variables

8p*2p-9*2p+2=0

Wy multiply elements

16p^2-18p+2=0

a = 16; b = -18; c = +2;
Δ = b2-4ac
Δ = -182-4·16·2
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-14}{2*16}=\frac{4}{32}
=1/8
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+14}{2*16}=\frac{32}{32}
=1
$