7/10p-4=-2/5p-9

Solution for 7/10p-4=-2/5p-9 equation:

7/10p-4=-2/5p-9

We move all terms to the left:

7/10p-4-(-2/5p-9)=0


Domain of the equation: 10p!=0

p!=0/10

p!=0

p∈R



Domain of the equation: 5p-9)!=0

p∈R


We get rid of parentheses

7/10p+2/5p+9-4=0

We calculate fractions


35p/50p^2+20p/50p^2+9-4=0

We add all the numbers together, and all the variables

35p/50p^2+20p/50p^2+5=0

We multiply all the terms by the denominator


35p+20p+5*50p^2=0

We add all the numbers together, and all the variables

55p+5*50p^2=0

Wy multiply elements

250p^2+55p=0

a = 250; b = 55; c = 0;
Δ = b2-4ac
Δ = 552-4·250·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-55}{2*250}=\frac{-110}{500}
=-11/50
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+55}{2*250}=\frac{0}{500}
=0
$