7/10p+3/2=3/5p+2

Solution for 7/10p+3/2=3/5p+2 equation:

7/10p+3/2=3/5p+2

We move all terms to the left:

7/10p+3/2-(3/5p+2)=0


Domain of the equation: 10p!=0

p!=0/10

p!=0

p∈R



Domain of the equation: 5p+2)!=0

p∈R


We get rid of parentheses

7/10p-3/5p-2+3/2=0

We calculate fractions


750p^2/200p^2+140p/200p^2+(-120p)/200p^2-2=0

We multiply all the terms by the denominator


750p^2+140p+(-120p)-2*200p^2=0

Wy multiply elements

750p^2-400p^2+140p+(-120p)=0

We get rid of parentheses

750p^2-400p^2+140p-120p=0

We add all the numbers together, and all the variables

350p^2+20p=0

a = 350; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·350·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*350}=\frac{-40}{700}
=-2/35
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*350}=\frac{0}{700}
=0
$