3/4x+1/3x=12

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

3/4x+1/3x=12

We move all terms to the left:

3/4x+1/3x-(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 calculate fractions


9x/12x^2+4x/12x^2-12=0

We multiply all the terms by the denominator


9x+4x-12*12x^2=0

We add all the numbers together, and all the variables

13x-12*12x^2=0

Wy multiply elements

-144x^2+13x=0

a = -144; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-144)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-144}=\frac{-26}{-288}
=13/144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-144}=\frac{0}{-288}
=0
$