8-1/2p=2/3p-10

Solution for 8-1/2p=2/3p-10 equation:

8-1/2p=2/3p-10

We move all terms to the left:

8-1/2p-(2/3p-10)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 3p-10)!=0

p∈R


We get rid of parentheses

-1/2p-2/3p+10+8=0

We calculate fractions


(-3p)/6p^2+(-4p)/6p^2+10+8=0

We add all the numbers together, and all the variables

(-3p)/6p^2+(-4p)/6p^2+18=0

We multiply all the terms by the denominator


(-3p)+(-4p)+18*6p^2=0

Wy multiply elements

108p^2+(-3p)+(-4p)=0

We get rid of parentheses

108p^2-3p-4p=0

We add all the numbers together, and all the variables

108p^2-7p=0

a = 108; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·108·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*108}=\frac{0}{216}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*108}=\frac{14}{216}
=7/108
$