1/6p+8=-13p+14

Solution for 1/6p+8=-13p+14 equation:

1/6p+8=-13p+14

We move all terms to the left:

1/6p+8-(-13p+14)=0


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R


We get rid of parentheses

1/6p+13p-14+8=0

We multiply all the terms by the denominator


13p*6p-14*6p+8*6p+1=0

Wy multiply elements

78p^2-84p+48p+1=0

We add all the numbers together, and all the variables

78p^2-36p+1=0

a = 78; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·78·1
Δ = 984
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:

$\sqrt{\Delta}=\sqrt{984}=\sqrt{4*246}=\sqrt{4}*\sqrt{246}=2\sqrt{246}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{246}}{2*78}=\frac{36-2\sqrt{246}}{156}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{246}}{2*78}=\frac{36+2\sqrt{246}}{156}
$