1/2p-13=3p+7

Solution for 1/2p-13=3p+7 equation:

1/2p-13=3p+7

We move all terms to the left:

1/2p-13-(3p+7)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

1/2p-3p-7-13=0

We multiply all the terms by the denominator


-3p*2p-7*2p-13*2p+1=0

Wy multiply elements

-6p^2-14p-26p+1=0

We add all the numbers together, and all the variables

-6p^2-40p+1=0

a = -6; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·(-6)·1
Δ = 1624
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:

$\sqrt{\Delta}=\sqrt{1624}=\sqrt{4*406}=\sqrt{4}*\sqrt{406}=2\sqrt{406}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{406}}{2*-6}=\frac{40-2\sqrt{406}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{406}}{2*-6}=\frac{40+2\sqrt{406}}{-12}
$