2/3p-7=1/4p+18

Solution for 2/3p-7=1/4p+18 equation:

2/3p-7=1/4p+18

We move all terms to the left:

2/3p-7-(1/4p+18)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 4p+18)!=0

p∈R


We get rid of parentheses

2/3p-1/4p-18-7=0

We calculate fractions


8p/12p^2+(-3p)/12p^2-18-7=0

We add all the numbers together, and all the variables

8p/12p^2+(-3p)/12p^2-25=0

We multiply all the terms by the denominator


8p+(-3p)-25*12p^2=0

Wy multiply elements

-300p^2+8p+(-3p)=0

We get rid of parentheses

-300p^2+8p-3p=0

We add all the numbers together, and all the variables

-300p^2+5p=0

a = -300; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-300)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-300}=\frac{-10}{-600}
=1/60
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-300}=\frac{0}{-600}
=0
$