9/2x+1/3=-1/6x+5

Solution for 9/2x+1/3=-1/6x+5 equation:

9/2x+1/3=-1/6x+5

We move all terms to the left:

9/2x+1/3-(-1/6x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x+5)!=0

x∈R


We get rid of parentheses

9/2x+1/6x-5+1/3=0

We calculate fractions


72x^2/108x^2+486x/108x^2+18x/108x^2-5=0

We multiply all the terms by the denominator


72x^2+486x+18x-5*108x^2=0

We add all the numbers together, and all the variables

72x^2+504x-5*108x^2=0

Wy multiply elements

72x^2-540x^2+504x=0

We add all the numbers together, and all the variables

-468x^2+504x=0

a = -468; b = 504; c = 0;
Δ = b2-4ac
Δ = 5042-4·(-468)·0
Δ = 254016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{254016}=504$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(504)-504}{2*-468}=\frac{-1008}{-936}
=1+1/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(504)+504}{2*-468}=\frac{0}{-936}
=0
$