1/4x+5/12x=4

Solution for 1/4x+5/12x=4 equation:

1/4x+5/12x=4

We move all terms to the left:

1/4x+5/12x-(4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We calculate fractions


12x/48x^2+20x/48x^2-4=0

We multiply all the terms by the denominator


12x+20x-4*48x^2=0

We add all the numbers together, and all the variables

32x-4*48x^2=0

Wy multiply elements

-192x^2+32x=0

a = -192; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-192)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-192}=\frac{-64}{-384}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-192}=\frac{0}{-384}
=0
$