1/5x-3=1/2x+9

Solution for 1/5x-3=1/2x+9 equation:

1/5x-3=1/2x+9

We move all terms to the left:

1/5x-3-(1/2x+9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x+9)!=0

x∈R


We get rid of parentheses

1/5x-1/2x-9-3=0

We calculate fractions


2x/10x^2+(-5x)/10x^2-9-3=0

We add all the numbers together, and all the variables

2x/10x^2+(-5x)/10x^2-12=0

We multiply all the terms by the denominator


2x+(-5x)-12*10x^2=0

Wy multiply elements

-120x^2+2x+(-5x)=0

We get rid of parentheses

-120x^2+2x-5x=0

We add all the numbers together, and all the variables

-120x^2-3x=0

a = -120; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-120)·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*-120}=\frac{0}{-240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-120}=\frac{6}{-240}
=-1/40
$