6+4/5p=9/10p

Solution for 6+4/5p=9/10p equation:

6+4/5p=9/10p

We move all terms to the left:

6+4/5p-(9/10p)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R



Domain of the equation: 10p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

4/5p-(+9/10p)+6=0

We get rid of parentheses

4/5p-9/10p+6=0

We calculate fractions


40p/50p^2+(-45p)/50p^2+6=0

We multiply all the terms by the denominator


40p+(-45p)+6*50p^2=0

Wy multiply elements

300p^2+40p+(-45p)=0

We get rid of parentheses

300p^2+40p-45p=0

We add all the numbers together, and all the variables

300p^2-5p=0

a = 300; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·300·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*300}=\frac{0}{600}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*300}=\frac{10}{600}
=1/60
$