(6p-12/p+3)+(5/p-2)=6

Solution for (6p-12/p+3)+(5/p-2)=6 equation:

(6p-12/p+3)+(5/p-2)=6

We move all terms to the left:

(6p-12/p+3)+(5/p-2)-(6)=0


Domain of the equation: p+3)!=0

p∈R



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

p∈R


We get rid of parentheses

6p-12/p+5/p+3-2-6=0

We multiply all the terms by the denominator


6p*p+3*p-2*p-6*p-12+5=0

We add all the numbers together, and all the variables

-5p+6p*p-7=0

Wy multiply elements

6p^2-5p-7=0

a = 6; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·6·(-7)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{193}}{2*6}=\frac{5-\sqrt{193}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{193}}{2*6}=\frac{5+\sqrt{193}}{12}
$