6/6p+4=3/4p-8

Solution for 6/6p+4=3/4p-8 equation:

6/6p+4=3/4p-8

We move all terms to the left:

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


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R



Domain of the equation: 4p-8)!=0

p∈R


We get rid of parentheses

6/6p-3/4p+8+4=0

We calculate fractions


24p/24p^2+(-18p)/24p^2+8+4=0

We add all the numbers together, and all the variables

24p/24p^2+(-18p)/24p^2+12=0

We multiply all the terms by the denominator


24p+(-18p)+12*24p^2=0

Wy multiply elements

288p^2+24p+(-18p)=0

We get rid of parentheses

288p^2+24p-18p=0

We add all the numbers together, and all the variables

288p^2+6p=0

a = 288; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·288·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*288}=\frac{-12}{576}
=-1/48
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*288}=\frac{0}{576}
=0
$