6p-16/p=3

Solution for 6p-16/p=3 equation:

6p-16/p=3

We move all terms to the left:

6p-16/p-(3)=0


Domain of the equation: p!=0

p∈R


We multiply all the terms by the denominator


6p*p-3*p-16=0

We add all the numbers together, and all the variables

-3p+6p*p-16=0

Wy multiply elements

6p^2-3p-16=0

a = 6; b = -3; c = -16;
Δ = b2-4ac
Δ = -32-4·6·(-16)
Δ = 393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{393}}{2*6}=\frac{3-\sqrt{393}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{393}}{2*6}=\frac{3+\sqrt{393}}{12}
$