3/4x-9=3/5x

Solution for 3/4x-9=3/5x equation:

3/4x-9=3/5x

We move all terms to the left:

3/4x-9-(3/5x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(+3/5x)-9=0

We get rid of parentheses

3/4x-3/5x-9=0

We calculate fractions


15x/20x^2+(-12x)/20x^2-9=0

We multiply all the terms by the denominator


15x+(-12x)-9*20x^2=0

Wy multiply elements

-180x^2+15x+(-12x)=0

We get rid of parentheses

-180x^2+15x-12x=0

We add all the numbers together, and all the variables

-180x^2+3x=0

a = -180; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-180)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-180}=\frac{-6}{-360}
=1/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-180}=\frac{0}{-360}
=0
$