1/3x+12=19-1/4x

Solution for 1/3x+12=19-1/4x equation:

1/3x+12=19-1/4x

We move all terms to the left:

1/3x+12-(19-1/4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(-1/4x+19)+12=0

We get rid of parentheses

1/3x+1/4x-19+12=0

We calculate fractions


4x/12x^2+3x/12x^2-19+12=0

We add all the numbers together, and all the variables

4x/12x^2+3x/12x^2-7=0

We multiply all the terms by the denominator


4x+3x-7*12x^2=0

We add all the numbers together, and all the variables

7x-7*12x^2=0

Wy multiply elements

-84x^2+7x=0

a = -84; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-84)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-84}=\frac{-14}{-168}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-84}=\frac{0}{-168}
=0
$