3/2p-14p=p+13

Solution for 3/2p-14p=p+13 equation:

3/2p-14p=p+13

We move all terms to the left:

3/2p-14p-(p+13)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We add all the numbers together, and all the variables

-14p+3/2p-(p+13)=0

We get rid of parentheses

-14p+3/2p-p-13=0

We multiply all the terms by the denominator


-14p*2p-p*2p-13*2p+3=0

Wy multiply elements

-28p^2-2p^2-26p+3=0

We add all the numbers together, and all the variables

-30p^2-26p+3=0

a = -30; b = -26; c = +3;
Δ = b2-4ac
Δ = -262-4·(-30)·3
Δ = 1036
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:

$\sqrt{\Delta}=\sqrt{1036}=\sqrt{4*259}=\sqrt{4}*\sqrt{259}=2\sqrt{259}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{259}}{2*-30}=\frac{26-2\sqrt{259}}{-60}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{259}}{2*-30}=\frac{26+2\sqrt{259}}{-60}
$