4/5p-3=3/10p+7

Solution for 4/5p-3=3/10p+7 equation:

4/5p-3=3/10p+7

We move all terms to the left:

4/5p-3-(3/10p+7)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R



Domain of the equation: 10p+7)!=0

p∈R


We get rid of parentheses

4/5p-3/10p-7-3=0

We calculate fractions


40p/50p^2+(-15p)/50p^2-7-3=0

We add all the numbers together, and all the variables

40p/50p^2+(-15p)/50p^2-10=0

We multiply all the terms by the denominator


40p+(-15p)-10*50p^2=0

Wy multiply elements

-500p^2+40p+(-15p)=0

We get rid of parentheses

-500p^2+40p-15p=0

We add all the numbers together, and all the variables

-500p^2+25p=0

a = -500; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-500)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-500}=\frac{-50}{-1000}
=1/20
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-500}=\frac{0}{-1000}
=0
$