-1/2p+3p=5

Solution for -1/2p+3p=5 equation:

-1/2p+3p=5

We move all terms to the left:

-1/2p+3p-(5)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

3p-1/2p-5=0

We multiply all the terms by the denominator


3p*2p-5*2p-1=0

Wy multiply elements

6p^2-10p-1=0

a = 6; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·6·(-1)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{31}}{2*6}=\frac{10-2\sqrt{31}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{31}}{2*6}=\frac{10+2\sqrt{31}}{12}
$