5/7p+3/4p=82

Solution for 5/7p+3/4p=82 equation:

5/7p+3/4p=82

We move all terms to the left:

5/7p+3/4p-(82)=0


Domain of the equation: 7p!=0

p!=0/7

p!=0

p∈R



Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We calculate fractions


20p/28p^2+21p/28p^2-82=0

We multiply all the terms by the denominator


20p+21p-82*28p^2=0

We add all the numbers together, and all the variables

41p-82*28p^2=0

Wy multiply elements

-2296p^2+41p=0

a = -2296; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-2296)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-2296}=\frac{-82}{-4592}
=1/56
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-2296}=\frac{0}{-4592}
=0
$