1/2x+4/3X=11/18

Solution for 1/2x+4/3X=11/18 equation:

1/2x+4/3x=11/18

We move all terms to the left:

1/2x+4/3x-(11/18)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+4/3x-(+11/18)=0

We get rid of parentheses

1/2x+4/3x-11/18=0

We calculate fractions


(-198x^2)/108x^2+54x/108x^2+144x/108x^2=0

We multiply all the terms by the denominator


(-198x^2)+54x+144x=0

We add all the numbers together, and all the variables

(-198x^2)+198x=0

We get rid of parentheses

-198x^2+198x=0

a = -198; b = 198; c = 0;
Δ = b2-4ac
Δ = 1982-4·(-198)·0
Δ = 39204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39204}=198$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(198)-198}{2*-198}=\frac{-396}{-396}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(198)+198}{2*-198}=\frac{0}{-396}
=0
$