1/2p-3=p-4

Solution for 1/2p-3=p-4 equation:

1/2p-3=p-4

We move all terms to the left:

1/2p-3-(p-4)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

1/2p-p+4-3=0

We multiply all the terms by the denominator


-p*2p+4*2p-3*2p+1=0

Wy multiply elements

-2p^2+8p-6p+1=0

We add all the numbers together, and all the variables

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

a = -2; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-2)·1
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{3}}{2*-2}=\frac{-2-2\sqrt{3}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{3}}{2*-2}=\frac{-2+2\sqrt{3}}{-4}
$