15+1/2p=3p

Solution for 15+1/2p=3p equation:

15+1/2p=3p

We move all terms to the left:

15+1/2p-(3p)=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+15=0

We multiply all the terms by the denominator


-3p*2p+15*2p+1=0

Wy multiply elements

-6p^2+30p+1=0

a = -6; b = 30; c = +1;
Δ = b2-4ac
Δ = 302-4·(-6)·1
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{231}}{2*-6}=\frac{-30-2\sqrt{231}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{231}}{2*-6}=\frac{-30+2\sqrt{231}}{-12}
$