7/p+2=-8/5p-4

Solution for 7/p+2=-8/5p-4 equation:

7/p+2=-8/5p-4

We move all terms to the left:

7/p+2-(-8/5p-4)=0


Domain of the equation: p!=0

p∈R



Domain of the equation: 5p-4)!=0

p∈R


We get rid of parentheses

7/p+8/5p+4+2=0

We calculate fractions


35p/5p^2+8p/5p^2+4+2=0

We add all the numbers together, and all the variables

35p/5p^2+8p/5p^2+6=0

We multiply all the terms by the denominator


35p+8p+6*5p^2=0

We add all the numbers together, and all the variables

43p+6*5p^2=0

Wy multiply elements

30p^2+43p=0

a = 30; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·30·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*30}=\frac{-86}{60}
=-1+13/30
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*30}=\frac{0}{60}
=0
$