1/3x+1/4x=7/24

Solution for 1/3x+1/4x=7/24 equation:

1/3x+1/4x=7/24

We move all terms to the left:

1/3x+1/4x-(7/24)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x+1/4x-(+7/24)=0

We get rid of parentheses

1/3x+1/4x-7/24=0

We calculate fractions


(-336x^2)/576x^2+192x/576x^2+144x/576x^2=0

We multiply all the terms by the denominator


(-336x^2)+192x+144x=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-336x^2+336x=0

a = -336; b = 336; c = 0;
Δ = b2-4ac
Δ = 3362-4·(-336)·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*-336}=\frac{-672}{-672}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(336)+336}{2*-336}=\frac{0}{-672}
=0
$