11/3x+3/2x=413/18

Solution for 11/3x+3/2x=413/18 equation:

11/3x+3/2x=413/18

We move all terms to the left:

11/3x+3/2x-(413/18)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

11/3x+3/2x-(+413/18)=0

We get rid of parentheses

11/3x+3/2x-413/18=0

We calculate fractions


(-4956x^2)/108x^2+396x/108x^2+162x/108x^2=0

We multiply all the terms by the denominator


(-4956x^2)+396x+162x=0

We add all the numbers together, and all the variables

(-4956x^2)+558x=0

We get rid of parentheses

-4956x^2+558x=0

a = -4956; b = 558; c = 0;
Δ = b2-4ac
Δ = 5582-4·(-4956)·0
Δ = 311364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{311364}=558$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(558)-558}{2*-4956}=\frac{-1116}{-9912}
=93/826
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(558)+558}{2*-4956}=\frac{0}{-9912}
=0
$