1x/2x+3=x-9

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

1x/2x+3=x-9

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


1x-x*2x+9*2x+3*2x=0

We add all the numbers together, and all the variables

x-x*2x+9*2x+3*2x=0

Wy multiply elements

-2x^2+x+18x+6x=0

We add all the numbers together, and all the variables

-2x^2+25x=0

a = -2; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-2)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-2}=\frac{-50}{-4}
=12+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-2}=\frac{0}{-4}
=0
$