3/8x+6=3/4x-12

Solution for 3/8x+6=3/4x-12 equation:

3/8x+6=3/4x-12

We move all terms to the left:

3/8x+6-(3/4x-12)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x-12)!=0

x∈R


We get rid of parentheses

3/8x-3/4x+12+6=0

We calculate fractions


12x/32x^2+(-24x)/32x^2+12+6=0

We add all the numbers together, and all the variables

12x/32x^2+(-24x)/32x^2+18=0

We multiply all the terms by the denominator


12x+(-24x)+18*32x^2=0

Wy multiply elements

576x^2+12x+(-24x)=0

We get rid of parentheses

576x^2+12x-24x=0

We add all the numbers together, and all the variables

576x^2-12x=0

a = 576; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·576·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*576}=\frac{0}{1152}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*576}=\frac{24}{1152}
=1/48
$