1/2x+1/3x=10/12

Solution for 1/2x+1/3x=10/12 equation:

1/2x+1/3x=10/12

We move all terms to the left:

1/2x+1/3x-(10/12)=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-(+10/12)=0

We get rid of parentheses

1/2x+1/3x-10/12=0

We calculate fractions


(-180x^2)/72x^2+36x/72x^2+24x/72x^2=0

We multiply all the terms by the denominator


(-180x^2)+36x+24x=0

We add all the numbers together, and all the variables

(-180x^2)+60x=0

We get rid of parentheses

-180x^2+60x=0

a = -180; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-180)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-180}=\frac{-120}{-360}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-180}=\frac{0}{-360}
=0
$