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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+9)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


5x/10x^2+(-4x)/10x^2-9-3=0

We add all the numbers together, and all the variables

5x/10x^2+(-4x)/10x^2-12=0

We multiply all the terms by the denominator


5x+(-4x)-12*10x^2=0

Wy multiply elements

-120x^2+5x+(-4x)=0

We get rid of parentheses

-120x^2+5x-4x=0

We add all the numbers together, and all the variables

-120x^2+x=0

a = -120; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-120)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-120}=\frac{-2}{-240}
=1/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-120}=\frac{0}{-240}
=0
$