285/p=13p+108

Solution for 285/p=13p+108 equation:

285/p=13p+108

We move all terms to the left:

285/p-(13p+108)=0


Domain of the equation: p!=0

p∈R


We get rid of parentheses

285/p-13p-108=0

We multiply all the terms by the denominator


-13p*p-108*p+285=0

We add all the numbers together, and all the variables

-108p-13p*p+285=0

Wy multiply elements

-13p^2-108p+285=0

a = -13; b = -108; c = +285;
Δ = b2-4ac
Δ = -1082-4·(-13)·285
Δ = 26484
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:

$\sqrt{\Delta}=\sqrt{26484}=\sqrt{4*6621}=\sqrt{4}*\sqrt{6621}=2\sqrt{6621}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{6621}}{2*-13}=\frac{108-2\sqrt{6621}}{-26}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{6621}}{2*-13}=\frac{108+2\sqrt{6621}}{-26}
$