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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-3x)/12x^2+(-8x)/12x^2-4+6=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

24x^2+(-3x)+(-8x)=0

We get rid of parentheses

24x^2-3x-8x=0

We add all the numbers together, and all the variables

24x^2-11x=0

a = 24; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·24·0
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*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*24}=\frac{22}{48}
=11/24
$