5p-1/2p=3

Solution for 5p-1/2p=3 equation:

5p-1/2p=3

We move all terms to the left:

5p-1/2p-(3)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We multiply all the terms by the denominator


5p*2p-3*2p-1=0

Wy multiply elements

10p^2-6p-1=0

a = 10; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·10·(-1)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*10}=\frac{6-2\sqrt{19}}{20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*10}=\frac{6+2\sqrt{19}}{20}
$