7/6p+p=234

Solution for 7/6p+p=234 equation:

7/6p+p=234

We move all terms to the left:

7/6p+p-(234)=0


Domain of the equation: 6p!=0

p!=0/6

p!=0

p∈R


We add all the numbers together, and all the variables

p+7/6p-234=0

We multiply all the terms by the denominator


p*6p-234*6p+7=0

Wy multiply elements

6p^2-1404p+7=0

a = 6; b = -1404; c = +7;
Δ = b2-4ac
Δ = -14042-4·6·7
Δ = 1971048
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:

$\sqrt{\Delta}=\sqrt{1971048}=\sqrt{4*492762}=\sqrt{4}*\sqrt{492762}=2\sqrt{492762}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1404)-2\sqrt{492762}}{2*6}=\frac{1404-2\sqrt{492762}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1404)+2\sqrt{492762}}{2*6}=\frac{1404+2\sqrt{492762}}{12}
$