1/2x+3/9x+1=12

Solution for 1/2x+3/9x+1=12 equation:

1/2x+3/9x+1=12

We move all terms to the left:

1/2x+3/9x+1-(12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+3/9x-11=0

We calculate fractions


9x/18x^2+6x/18x^2-11=0

We multiply all the terms by the denominator


9x+6x-11*18x^2=0

We add all the numbers together, and all the variables

15x-11*18x^2=0

Wy multiply elements

-198x^2+15x=0

a = -198; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-198)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-198}=\frac{-30}{-396}
=5/66
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-198}=\frac{0}{-396}
=0
$