4+2p=3/5p-2

Solution for 4+2p=3/5p-2 equation:

4+2p=3/5p-2

We move all terms to the left:

4+2p-(3/5p-2)=0


Domain of the equation: 5p-2)!=0

p∈R


We get rid of parentheses

2p-3/5p+2+4=0

We multiply all the terms by the denominator


2p*5p+2*5p+4*5p-3=0

Wy multiply elements

10p^2+10p+20p-3=0

We add all the numbers together, and all the variables

10p^2+30p-3=0

a = 10; b = 30; c = -3;
Δ = b2-4ac
Δ = 302-4·10·(-3)
Δ = 1020
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:

$\sqrt{\Delta}=\sqrt{1020}=\sqrt{4*255}=\sqrt{4}*\sqrt{255}=2\sqrt{255}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{255}}{2*10}=\frac{-30-2\sqrt{255}}{20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{255}}{2*10}=\frac{-30+2\sqrt{255}}{20}
$