3x/x+9=x/5

Solution for 3x/x+9=x/5 equation:

3x/x+9=x/5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-1x^2)/5x+15x/5x+9=0

We multiply all the terms by the denominator


(-1x^2)+15x+9*5x=0

Wy multiply elements

(-1x^2)+15x+45x=0

We get rid of parentheses

-1x^2+15x+45x=0

We add all the numbers together, and all the variables

-1x^2+60x=0

a = -1; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-1)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-1}=\frac{-120}{-2}
=+60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-1}=\frac{0}{-2}
=0
$