2/3x+1/8=3/4x+12

Solution for 2/3x+1/8=3/4x+12 equation:

2/3x+1/8=3/4x+12

We move all terms to the left:

2/3x+1/8-(3/4x+12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

2/3x-3/4x-12+1/8=0

We calculate fractions


48x^2/768x^2+512x/768x^2+(-576x)/768x^2-12=0

We multiply all the terms by the denominator


48x^2+512x+(-576x)-12*768x^2=0

Wy multiply elements

48x^2-9216x^2+512x+(-576x)=0

We get rid of parentheses

48x^2-9216x^2+512x-576x=0

We add all the numbers together, and all the variables

-9168x^2-64x=0

a = -9168; b = -64; c = 0;
Δ = b2-4ac
Δ = -642-4·(-9168)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-64}{2*-9168}=\frac{0}{-18336}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+64}{2*-9168}=\frac{128}{-18336}
=-4/573
$