4/3p-1/2p=10

Solution for 4/3p-1/2p=10 equation:

4/3p-1/2p=10

We move all terms to the left:

4/3p-1/2p-(10)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We calculate fractions


8p/6p^2+(-3p)/6p^2-10=0

We multiply all the terms by the denominator


8p+(-3p)-10*6p^2=0

Wy multiply elements

-60p^2+8p+(-3p)=0

We get rid of parentheses

-60p^2+8p-3p=0

We add all the numbers together, and all the variables

-60p^2+5p=0

a = -60; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-60)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-60}=\frac{-10}{-120}
=1/12
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-60}=\frac{0}{-120}
=0
$