1/4p+2/5p=9/20

Solution for 1/4p+2/5p=9/20 equation:

1/4p+2/5p=9/20

We move all terms to the left:

1/4p+2/5p-(9/20)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We add all the numbers together, and all the variables

1/4p+2/5p-(+9/20)=0

We get rid of parentheses

1/4p+2/5p-9/20=0

We calculate fractions


(-900p^2)/800p^2+200p/800p^2+320p/800p^2=0

We multiply all the terms by the denominator


(-900p^2)+200p+320p=0

We add all the numbers together, and all the variables

(-900p^2)+520p=0

We get rid of parentheses

-900p^2+520p=0

a = -900; b = 520; c = 0;
Δ = b2-4ac
Δ = 5202-4·(-900)·0
Δ = 270400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{270400}=520$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(520)-520}{2*-900}=\frac{-1040}{-1800}
=26/45
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(520)+520}{2*-900}=\frac{0}{-1800}
=0
$