3/4p=4/5p+10

Solution for 3/4p=4/5p+10 equation:

3/4p=4/5p+10

We move all terms to the left:

3/4p-(4/5p+10)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 5p+10)!=0

p∈R


We get rid of parentheses

3/4p-4/5p-10=0

We calculate fractions


15p/20p^2+(-16p)/20p^2-10=0

We multiply all the terms by the denominator


15p+(-16p)-10*20p^2=0

Wy multiply elements

-200p^2+15p+(-16p)=0

We get rid of parentheses

-200p^2+15p-16p=0

We add all the numbers together, and all the variables

-200p^2-1p=0

a = -200; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-200)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-200}=\frac{0}{-400}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-200}=\frac{2}{-400}
=-1/200
$