8/4x-6=4-1/12x

Solution for 8/4x-6=4-1/12x equation:

8/4x-6=4-1/12x

We move all terms to the left:

8/4x-6-(4-1/12x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8/4x-(-1/12x+4)-6=0

We get rid of parentheses

8/4x+1/12x-4-6=0

We calculate fractions


96x/48x^2+4x/48x^2-4-6=0

We add all the numbers together, and all the variables

96x/48x^2+4x/48x^2-10=0

We multiply all the terms by the denominator


96x+4x-10*48x^2=0

We add all the numbers together, and all the variables

100x-10*48x^2=0

Wy multiply elements

-480x^2+100x=0

a = -480; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·(-480)·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*-480}=\frac{-200}{-960}
=5/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*-480}=\frac{0}{-960}
=0
$