1/2p+1=7p-14

Solution for 1/2p+1=7p-14 equation:

1/2p+1=7p-14

We move all terms to the left:

1/2p+1-(7p-14)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

1/2p-7p+14+1=0

We multiply all the terms by the denominator


-7p*2p+14*2p+1*2p+1=0

Wy multiply elements

-14p^2+28p+2p+1=0

We add all the numbers together, and all the variables

-14p^2+30p+1=0

a = -14; b = 30; c = +1;
Δ = b2-4ac
Δ = 302-4·(-14)·1
Δ = 956
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:

$\sqrt{\Delta}=\sqrt{956}=\sqrt{4*239}=\sqrt{4}*\sqrt{239}=2\sqrt{239}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{239}}{2*-14}=\frac{-30-2\sqrt{239}}{-28}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{239}}{2*-14}=\frac{-30+2\sqrt{239}}{-28}
$