x/4x+6=3x-4

Solution for x/4x+6=3x-4 equation:

x/4x+6=3x-4

We move all terms to the left:

x/4x+6-(3x-4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

x/4x-3x+4+6=0

We multiply all the terms by the denominator


x-3x*4x+4*4x+6*4x=0

Wy multiply elements

-12x^2+x+16x+24x=0

We add all the numbers together, and all the variables

-12x^2+41x=0

a = -12; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-12)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-12}=\frac{-82}{-24}
=3+5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-12}=\frac{0}{-24}
=0
$