2/x+7/9x=25/27

Solution for 2/x+7/9x=25/27 equation:

2/x+7/9x=25/27

We move all terms to the left:

2/x+7/9x-(25/27)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+7/9x-(+25/27)=0

We get rid of parentheses

2/x+7/9x-25/27=0

We calculate fractions


(-2025x^2)/486x^2+972x/486x^2+378x/486x^2=0

We multiply all the terms by the denominator


(-2025x^2)+972x+378x=0

We add all the numbers together, and all the variables

(-2025x^2)+1350x=0

We get rid of parentheses

-2025x^2+1350x=0

a = -2025; b = 1350; c = 0;
Δ = b2-4ac
Δ = 13502-4·(-2025)·0
Δ = 1822500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1822500}=1350$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1350)-1350}{2*-2025}=\frac{-2700}{-4050}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1350)+1350}{2*-2025}=\frac{0}{-4050}
=0
$