7/10p-2/5p=3

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

7/10p-2/5p=3

We move all terms to the left:

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


Domain of the equation: 10p!=0

p!=0/10

p!=0

p∈R



Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We calculate fractions


35p/50p^2+(-20p)/50p^2-3=0

We multiply all the terms by the denominator


35p+(-20p)-3*50p^2=0

Wy multiply elements

-150p^2+35p+(-20p)=0

We get rid of parentheses

-150p^2+35p-20p=0

We add all the numbers together, and all the variables

-150p^2+15p=0

a = -150; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-150)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-150}=\frac{-30}{-300}
=1/10
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-150}=\frac{0}{-300}
=0
$