1/4x+2=2/3x-6

Solution for 1/4x+2=2/3x-6 equation:

1/4x+2=2/3x-6

We move all terms to the left:

1/4x+2-(2/3x-6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-6)!=0

x∈R


We get rid of parentheses

1/4x-2/3x+6+2=0

We calculate fractions


3x/12x^2+(-8x)/12x^2+6+2=0

We add all the numbers together, and all the variables

3x/12x^2+(-8x)/12x^2+8=0

We multiply all the terms by the denominator


3x+(-8x)+8*12x^2=0

Wy multiply elements

96x^2+3x+(-8x)=0

We get rid of parentheses

96x^2+3x-8x=0

We add all the numbers together, and all the variables

96x^2-5x=0

a = 96; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·96·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*96}=\frac{0}{192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*96}=\frac{10}{192}
=5/96
$