1/6p-8/15=2/3p+3

Solution for 1/6p-8/15=2/3p+3 equation:

1/6p-8/15=2/3p+3

We move all terms to the left:

1/6p-8/15-(2/3p+3)=0


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R



Domain of the equation: 3p+3)!=0

p∈R


We get rid of parentheses

1/6p-2/3p-3-8/15=0

We calculate fractions


(-432p^2)/270p^2+45p/270p^2+(-180p)/270p^2-3=0

We multiply all the terms by the denominator


(-432p^2)+45p+(-180p)-3*270p^2=0

Wy multiply elements

(-432p^2)-810p^2+45p+(-180p)=0

We get rid of parentheses

-432p^2-810p^2+45p-180p=0

We add all the numbers together, and all the variables

-1242p^2-135p=0

a = -1242; b = -135; c = 0;
Δ = b2-4ac
Δ = -1352-4·(-1242)·0
Δ = 18225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18225}=135$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-135}{2*-1242}=\frac{0}{-2484}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+135}{2*-1242}=\frac{270}{-2484}
=-5/46
$