3/4x+4/12x=-12

Solution for 3/4x+4/12x=-12 equation:

3/4x+4/12x=-12

We move all terms to the left:

3/4x+4/12x-(-12)=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 add all the numbers together, and all the variables

3/4x+4/12x+12=0

We calculate fractions


36x/48x^2+16x/48x^2+12=0

We multiply all the terms by the denominator


36x+16x+12*48x^2=0

We add all the numbers together, and all the variables

52x+12*48x^2=0

Wy multiply elements

576x^2+52x=0

a = 576; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·576·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*576}=\frac{-104}{1152}
=-13/144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*576}=\frac{0}{1152}
=0
$