21p-7/p=46

Solution for 21p-7/p=46 equation:

21p-7/p=46

We move all terms to the left:

21p-7/p-(46)=0


Domain of the equation: p!=0

p∈R


We multiply all the terms by the denominator


21p*p-46*p-7=0

We add all the numbers together, and all the variables

-46p+21p*p-7=0

Wy multiply elements

21p^2-46p-7=0

a = 21; b = -46; c = -7;
Δ = b2-4ac
Δ = -462-4·21·(-7)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-52}{2*21}=\frac{-6}{42}
=-1/7
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+52}{2*21}=\frac{98}{42}
=2+1/3
$