6(1/6p-5)=6(1/2p+2)

Solution for 6(1/6p-5)=6(1/2p+2) equation:

6(1/6p-5)=6(1/2p+2)

We move all terms to the left:

6(1/6p-5)-(6(1/2p+2))=0


Domain of the equation: 6p-5)!=0

p∈R



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

p∈R


We multiply parentheses

6p-(6(1/2p+2))-30=0

We multiply all the terms by the denominator


6p*2p-30*2p+2))-(6(1+2))=0

We add all the numbers together, and all the variables

6p*2p-30*2p+2))-(63)=0

We add all the numbers together, and all the variables

6p*2p-30*2p=0

Wy multiply elements

12p^2-60p=0

a = 12; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·12·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*12}=\frac{0}{24}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*12}=\frac{120}{24}
=5
$