p/5p+7-4p=-21

Solution for p/5p+7-4p=-21 equation:

p/5p+7-4p=-21

We move all terms to the left:

p/5p+7-4p-(-21)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We add all the numbers together, and all the variables

-4p+p/5p+28=0

We multiply all the terms by the denominator


-4p*5p+p+28*5p=0

We add all the numbers together, and all the variables

p-4p*5p+28*5p=0

Wy multiply elements

-20p^2+p+140p=0

We add all the numbers together, and all the variables

-20p^2+141p=0

a = -20; b = 141; c = 0;
Δ = b2-4ac
Δ = 1412-4·(-20)·0
Δ = 19881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19881}=141$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(141)-141}{2*-20}=\frac{-282}{-40}
=7+1/20
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(141)+141}{2*-20}=\frac{0}{-40}
=0
$