5/6p+1/3p-1/2=6*1/2

Solution for 5/6p+1/3p-1/2=6*1/2 equation:

5/6p+1/3p-1/2=6*1/2

We move all terms to the left:

5/6p+1/3p-1/2-(6*1/2)=0


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R



Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We add all the numbers together, and all the variables

5/6p+1/3p-1/2-3=0

We add all the numbers together, and all the variables

5/6p+1/3p-3-1/2=0

We calculate fractions


(-54p^2)/72p^2+60p/72p^2+24p/72p^2-3=0

We multiply all the terms by the denominator


(-54p^2)+60p+24p-3*72p^2=0

We add all the numbers together, and all the variables

(-54p^2)+84p-3*72p^2=0

Wy multiply elements

(-54p^2)-216p^2+84p=0

We get rid of parentheses

-54p^2-216p^2+84p=0

We add all the numbers together, and all the variables

-270p^2+84p=0

a = -270; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·(-270)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*-270}=\frac{-168}{-540}
=14/45
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*-270}=\frac{0}{-540}
=0
$