1/4x+1/3x+1/4=17/12

Solution for 1/4x+1/3x+1/4=17/12 equation:

1/4x+1/3x+1/4=17/12

We move all terms to the left:

1/4x+1/3x+1/4-(17/12)=0


Domain of the equation: 4x!=0

x!=0/4

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

1/4x+1/3x+1/4-(+17/12)=0

We get rid of parentheses

1/4x+1/3x+1/4-17/12=0

We calculate fractions


(-2448x^2)/2304x^2+36x/2304x^2+768x/2304x^2+36x/2304x^2=0

We multiply all the terms by the denominator


(-2448x^2)+36x+768x+36x=0

We add all the numbers together, and all the variables

(-2448x^2)+840x=0

We get rid of parentheses

-2448x^2+840x=0

a = -2448; b = 840; c = 0;
Δ = b2-4ac
Δ = 8402-4·(-2448)·0
Δ = 705600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{705600}=840$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(840)-840}{2*-2448}=\frac{-1680}{-4896}
=35/102
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(840)+840}{2*-2448}=\frac{0}{-4896}
=0
$