-1/4p+9/5p+6=30

Solution for -1/4p+9/5p+6=30 equation:

-1/4p+9/5p+6=30

We move all terms to the left:

-1/4p+9/5p+6-(30)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We add all the numbers together, and all the variables

-1/4p+9/5p-24=0

We calculate fractions


(-5p)/20p^2+36p/20p^2-24=0

We multiply all the terms by the denominator


(-5p)+36p-24*20p^2=0

We add all the numbers together, and all the variables

36p+(-5p)-24*20p^2=0

Wy multiply elements

-480p^2+36p+(-5p)=0

We get rid of parentheses

-480p^2+36p-5p=0

We add all the numbers together, and all the variables

-480p^2+31p=0

a = -480; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-480)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-480}=\frac{-62}{-960}
=31/480
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-480}=\frac{0}{-960}
=0
$