5/8p+1/4p=2

Solution for 5/8p+1/4p=2 equation:

5/8p+1/4p=2

We move all terms to the left:

5/8p+1/4p-(2)=0


Domain of the equation: 8p!=0

p!=0/8

p!=0

p∈R



Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We calculate fractions


20p/32p^2+8p/32p^2-2=0

We multiply all the terms by the denominator


20p+8p-2*32p^2=0

We add all the numbers together, and all the variables

28p-2*32p^2=0

Wy multiply elements

-64p^2+28p=0

a = -64; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-64)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-64}=\frac{-56}{-128}
=7/16
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-64}=\frac{0}{-128}
=0
$