9/6x-1=6/25x

Solution for 9/6x-1=6/25x equation:

9/6x-1=6/25x

We move all terms to the left:

9/6x-1-(6/25x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 25x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9/6x-(+6/25x)-1=0

We get rid of parentheses

9/6x-6/25x-1=0

We calculate fractions


225x/150x^2+(-36x)/150x^2-1=0

We multiply all the terms by the denominator


225x+(-36x)-1*150x^2=0

Wy multiply elements

-150x^2+225x+(-36x)=0

We get rid of parentheses

-150x^2+225x-36x=0

We add all the numbers together, and all the variables

-150x^2+189x=0

a = -150; b = 189; c = 0;
Δ = b2-4ac
Δ = 1892-4·(-150)·0
Δ = 35721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35721}=189$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(189)-189}{2*-150}=\frac{-378}{-300}
=1+13/50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(189)+189}{2*-150}=\frac{0}{-300}
=0
$