1/4x=7-1/3x

Solution for 1/4x=7-1/3x equation:

1/4x=7-1/3x

We move all terms to the left:

1/4x-(7-1/3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(-1/3x+7)=0

We get rid of parentheses

1/4x+1/3x-7=0

We calculate fractions


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

We multiply all the terms by the denominator


3x+4x-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
$