16-3p=2/3p*5

Solution for 16-3p=2/3p*5 equation:

16-3p=2/3p*5

We move all terms to the left:

16-3p-(2/3p*5)=0


Domain of the equation: 3p*5)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

-3p-(+2/3p*5)+16=0

We get rid of parentheses

-3p-2/3p*5+16=0

We multiply all the terms by the denominator


-3p*3p*5+16*3p*5-2=0

Wy multiply elements

-45p^2*5+240p*5-2=0

Wy multiply elements

-225p^2+1200p-2=0

a = -225; b = 1200; c = -2;
Δ = b2-4ac
Δ = 12002-4·(-225)·(-2)
Δ = 1438200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1438200}=\sqrt{900*1598}=\sqrt{900}*\sqrt{1598}=30\sqrt{1598}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1200)-30\sqrt{1598}}{2*-225}=\frac{-1200-30\sqrt{1598}}{-450}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1200)+30\sqrt{1598}}{2*-225}=\frac{-1200+30\sqrt{1598}}{-450}
$