2/5p-11/15=1/10p-4

Solution for 2/5p-11/15=1/10p-4 equation:

2/5p-11/15=1/10p-4

We move all terms to the left:

2/5p-11/15-(1/10p-4)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R



Domain of the equation: 10p-4)!=0

p∈R


We get rid of parentheses

2/5p-1/10p+4-11/15=0

We calculate fractions


(-550p^2)/750p^2+300p/750p^2+(-75p)/750p^2+4=0

We multiply all the terms by the denominator


(-550p^2)+300p+(-75p)+4*750p^2=0

Wy multiply elements

(-550p^2)+3000p^2+300p+(-75p)=0

We get rid of parentheses

-550p^2+3000p^2+300p-75p=0

We add all the numbers together, and all the variables

2450p^2+225p=0

a = 2450; b = 225; c = 0;
Δ = b2-4ac
Δ = 2252-4·2450·0
Δ = 50625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50625}=225$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(225)-225}{2*2450}=\frac{-450}{4900}
=-9/98
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(225)+225}{2*2450}=\frac{0}{4900}
=0
$