8/3p-6+16/5p=18

Solution for 8/3p-6+16/5p=18 equation:

8/3p-6+16/5p=18

We move all terms to the left:

8/3p-6+16/5p-(18)=0


Domain of the equation: 3p!=0

p!=0/3

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

8/3p+16/5p-24=0

We calculate fractions


40p/15p^2+48p/15p^2-24=0

We multiply all the terms by the denominator


40p+48p-24*15p^2=0

We add all the numbers together, and all the variables

88p-24*15p^2=0

Wy multiply elements

-360p^2+88p=0

a = -360; b = 88; c = 0;
Δ = b2-4ac
Δ = 882-4·(-360)·0
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-88}{2*-360}=\frac{-176}{-720}
=11/45
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+88}{2*-360}=\frac{0}{-720}
=0
$