7-1/2p=3p

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

7-1/2p=3p

We move all terms to the left:

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -6; b = 14; c = -1;
Δ = b2-4ac
Δ = 142-4·(-6)·(-1)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{43}}{2*-6}=\frac{-14-2\sqrt{43}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{43}}{2*-6}=\frac{-14+2\sqrt{43}}{-12}
$