3/2p-14=p*13

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

3/2p-14=p*13

We move all terms to the left:

3/2p-14-(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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

-26p^2-14*2p+3=0

Wy multiply elements

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

a = -26; b = -28; c = +3;
Δ = b2-4ac
Δ = -282-4·(-26)·3
Δ = 1096
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:

$\sqrt{\Delta}=\sqrt{1096}=\sqrt{4*274}=\sqrt{4}*\sqrt{274}=2\sqrt{274}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{274}}{2*-26}=\frac{28-2\sqrt{274}}{-52}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{274}}{2*-26}=\frac{28+2\sqrt{274}}{-52}
$