2/3x+1/2x=7/24

Solution for 2/3x+1/2x=7/24 equation:

2/3x+1/2x=7/24

We move all terms to the left:

2/3x+1/2x-(7/24)=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

2/3x+1/2x-(+7/24)=0

We get rid of parentheses

2/3x+1/2x-7/24=0

We calculate fractions


(-84x^2)/288x^2+192x/288x^2+144x/288x^2=0

We multiply all the terms by the denominator


(-84x^2)+192x+144x=0

We add all the numbers together, and all the variables

(-84x^2)+336x=0

We get rid of parentheses

-84x^2+336x=0

a = -84; b = 336; c = 0;
Δ = b2-4ac
Δ = 3362-4·(-84)·0
Δ = 112896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{112896}=336$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(336)-336}{2*-84}=\frac{-672}{-168}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(336)+336}{2*-84}=\frac{0}{-168}
=0
$