3/4p-5/6=2/3p

Solution for 3/4p-5/6=2/3p equation:

3/4p-5/6=2/3p

We move all terms to the left:

3/4p-5/6-(2/3p)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

3/4p-(+2/3p)-5/6=0

We get rid of parentheses

3/4p-2/3p-5/6=0

We calculate fractions


(-180p^2)/432p^2+324p/432p^2+(-288p)/432p^2=0

We multiply all the terms by the denominator


(-180p^2)+324p+(-288p)=0

We get rid of parentheses

-180p^2+324p-288p=0

We add all the numbers together, and all the variables

-180p^2+36p=0

a = -180; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-180)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-180}=\frac{-72}{-360}
=1/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-180}=\frac{0}{-360}
=0
$