2p+3/3p-7=0

Solution for 2p+3/3p-7=0 equation:

2p+3/3p-7=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We multiply all the terms by the denominator


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

Wy multiply elements

6p^2-21p+3=0

a = 6; b = -21; c = +3;
Δ = b2-4ac
Δ = -212-4·6·3
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{41}}{2*6}=\frac{21-3\sqrt{41}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{41}}{2*6}=\frac{21+3\sqrt{41}}{12}
$