-1/4x+6=2/3x+38

Solution for -1/4x+6=2/3x+38 equation:

-1/4x+6=2/3x+38

We move all terms to the left:

-1/4x+6-(2/3x+38)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+38)!=0

x∈R


We get rid of parentheses

-1/4x-2/3x-38+6=0

We calculate fractions


(-3x)/12x^2+(-8x)/12x^2-38+6=0

We add all the numbers together, and all the variables

(-3x)/12x^2+(-8x)/12x^2-32=0

We multiply all the terms by the denominator


(-3x)+(-8x)-32*12x^2=0

Wy multiply elements

-384x^2+(-3x)+(-8x)=0

We get rid of parentheses

-384x^2-3x-8x=0

We add all the numbers together, and all the variables

-384x^2-11x=0

a = -384; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-384)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-384}=\frac{0}{-768}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-384}=\frac{22}{-768}
=-11/384
$