4/5p+6=-1/3p-3

Solution for 4/5p+6=-1/3p-3 equation:

4/5p+6=-1/3p-3

We move all terms to the left:

4/5p+6-(-1/3p-3)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R



Domain of the equation: 3p-3)!=0

p∈R


We get rid of parentheses

4/5p+1/3p+3+6=0

We calculate fractions


12p/15p^2+5p/15p^2+3+6=0

We add all the numbers together, and all the variables

12p/15p^2+5p/15p^2+9=0

We multiply all the terms by the denominator


12p+5p+9*15p^2=0

We add all the numbers together, and all the variables

17p+9*15p^2=0

Wy multiply elements

135p^2+17p=0

a = 135; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·135·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*135}=\frac{-34}{270}
=-17/135
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*135}=\frac{0}{270}
=0
$