1/3x+1/4x+1/3=25/12

Solution for 1/3x+1/4x+1/3=25/12 equation:

1/3x+1/4x+1/3=25/12

We move all terms to the left:

1/3x+1/4x+1/3-(25/12)=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+1/3-(+25/12)=0

We get rid of parentheses

1/3x+1/4x+1/3-25/12=0

We calculate fractions


(-3600x^2)/1296x^2+48x/1296x^2+324x/1296x^2+48x/1296x^2=0

We multiply all the terms by the denominator


(-3600x^2)+48x+324x+48x=0

We add all the numbers together, and all the variables

(-3600x^2)+420x=0

We get rid of parentheses

-3600x^2+420x=0

a = -3600; b = 420; c = 0;
Δ = b2-4ac
Δ = 4202-4·(-3600)·0
Δ = 176400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{176400}=420$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(420)-420}{2*-3600}=\frac{-840}{-7200}
=7/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(420)+420}{2*-3600}=\frac{0}{-7200}
=0
$