1/2+1/2x+1/3x=11/12

Solution for 1/2+1/2x+1/3x=11/12 equation:

1/2+1/2x+1/3x=11/12

We move all terms to the left:

1/2+1/2x+1/3x-(11/12)=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+1/3x+1/2-(+11/12)=0

We get rid of parentheses

1/2x+1/3x+1/2-11/12=0

We calculate fractions


(-396x^2)/288x^2+36x/288x^2+96x/288x^2+36x/288x^2=0

We multiply all the terms by the denominator


(-396x^2)+36x+96x+36x=0

We add all the numbers together, and all the variables

(-396x^2)+168x=0

We get rid of parentheses

-396x^2+168x=0

a = -396; b = 168; c = 0;
Δ = b2-4ac
Δ = 1682-4·(-396)·0
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-168}{2*-396}=\frac{-336}{-792}
=14/33
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+168}{2*-396}=\frac{0}{-792}
=0
$