2p-(7-5p)/9p-(3+4p)=7/6

Solution for 2p-(7-5p)/9p-(3+4p)=7/6 equation:

2p-(7-5p)/9p-(3+4p)=7/6

We move all terms to the left:

2p-(7-5p)/9p-(3+4p)-(7/6)=0


Domain of the equation: 9p!=0

p!=0/9

p!=0

p∈R


We add all the numbers together, and all the variables

2p-(-5p+7)/9p-(4p+3)-(+7/6)=0

We get rid of parentheses

2p-(-5p+7)/9p-4p-3-7/6=0

We calculate fractions


2p-4p+(30p-42)/54p+(-63p)/54p-3=0

We add all the numbers together, and all the variables

-2p+(30p-42)/54p+(-63p)/54p-3=0

We multiply all the terms by the denominator


-2p*54p+(30p-42)+(-63p)-3*54p=0

Wy multiply elements

-108p^2+(30p-42)+(-63p)-162p=0

We get rid of parentheses

-108p^2+30p-63p-162p-42=0

We add all the numbers together, and all the variables

-108p^2-195p-42=0

a = -108; b = -195; c = -42;
Δ = b2-4ac
Δ = -1952-4·(-108)·(-42)
Δ = 19881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19881}=141$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-195)-141}{2*-108}=\frac{54}{-216}
=-1/4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-195)+141}{2*-108}=\frac{336}{-216}
=-1+5/9
$