1/2x+2/3x=7/12

Solution for 1/2x+2/3x=7/12 equation:

1/2x+2/3x=7/12

We move all terms to the left:

1/2x+2/3x-(7/12)=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+2/3x-(+7/12)=0

We get rid of parentheses

1/2x+2/3x-7/12=0

We calculate fractions


(-126x^2)/72x^2+36x/72x^2+48x/72x^2=0

We multiply all the terms by the denominator


(-126x^2)+36x+48x=0

We add all the numbers together, and all the variables

(-126x^2)+84x=0

We get rid of parentheses

-126x^2+84x=0

a = -126; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·(-126)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*-126}=\frac{-168}{-252}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*-126}=\frac{0}{-252}
=0
$