7/10p-8=1/5p-6

Solution for 7/10p-8=1/5p-6 equation:

7/10p-8=1/5p-6

We move all terms to the left:

7/10p-8-(1/5p-6)=0


Domain of the equation: 10p!=0

p!=0/10

p!=0

p∈R



Domain of the equation: 5p-6)!=0

p∈R


We get rid of parentheses

7/10p-1/5p+6-8=0

We calculate fractions


35p/50p^2+(-10p)/50p^2+6-8=0

We add all the numbers together, and all the variables

35p/50p^2+(-10p)/50p^2-2=0

We multiply all the terms by the denominator


35p+(-10p)-2*50p^2=0

Wy multiply elements

-100p^2+35p+(-10p)=0

We get rid of parentheses

-100p^2+35p-10p=0

We add all the numbers together, and all the variables

-100p^2+25p=0

a = -100; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-100)·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*-100}=\frac{-50}{-200}
=1/4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-100}=\frac{0}{-200}
=0
$