1/5p-9=4/9p-29

Solution for 1/5p-9=4/9p-29 equation:

1/5p-9=4/9p-29

We move all terms to the left:

1/5p-9-(4/9p-29)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R



Domain of the equation: 9p-29)!=0

p∈R


We get rid of parentheses

1/5p-4/9p+29-9=0

We calculate fractions


9p/45p^2+(-20p)/45p^2+29-9=0

We add all the numbers together, and all the variables

9p/45p^2+(-20p)/45p^2+20=0

We multiply all the terms by the denominator


9p+(-20p)+20*45p^2=0

Wy multiply elements

900p^2+9p+(-20p)=0

We get rid of parentheses

900p^2+9p-20p=0

We add all the numbers together, and all the variables

900p^2-11p=0

a = 900; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·900·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*900}=\frac{0}{1800}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*900}=\frac{22}{1800}
=11/900
$