4/p-3=2p+8

Solution for 4/p-3=2p+8 equation:

4/p-3=2p+8

We move all terms to the left:

4/p-3-(2p+8)=0


Domain of the equation: p!=0

p∈R


We get rid of parentheses

4/p-2p-8-3=0

We multiply all the terms by the denominator


-2p*p-8*p-3*p+4=0

We add all the numbers together, and all the variables

-11p-2p*p+4=0

Wy multiply elements

-2p^2-11p+4=0

a = -2; b = -11; c = +4;
Δ = b2-4ac
Δ = -112-4·(-2)·4
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{17}}{2*-2}=\frac{11-3\sqrt{17}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{17}}{2*-2}=\frac{11+3\sqrt{17}}{-4}
$