P=3p-10/p

Solution for P=3p-10/p equation:

=3P-10/P

We move all terms to the left:

-(3P-10/P)=0


Domain of the equation: P)!=0

P!=0/1

P!=0

P∈R


We add all the numbers together, and all the variables

-(+3P-10/P)=0

We get rid of parentheses

-3P+10/P=0

We multiply all the terms by the denominator


-3P*P+10=0

Wy multiply elements

-3P^2+10=0

a = -3; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-3)·10
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-3}=\frac{0-2\sqrt{30}}{-6}
=-\frac{2\sqrt{30}}{-6}
=-\frac{\sqrt{30}}{-3}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-3}=\frac{0+2\sqrt{30}}{-6}
=\frac{2\sqrt{30}}{-6}
=\frac{\sqrt{30}}{-3}
$