10-2/3x=1/4x

Solution for 10-2/3x=1/4x equation:

10-2/3x=1/4x

We move all terms to the left:

10-2/3x-(1/4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-2/3x-(+1/4x)+10=0

We get rid of parentheses

-2/3x-1/4x+10=0

We calculate fractions


(-8x)/12x^2+(-3x)/12x^2+10=0

We multiply all the terms by the denominator


(-8x)+(-3x)+10*12x^2=0

Wy multiply elements

120x^2+(-8x)+(-3x)=0

We get rid of parentheses

120x^2-8x-3x=0

We add all the numbers together, and all the variables

120x^2-11x=0

a = 120; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·120·0
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*120}=\frac{0}{240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*120}=\frac{22}{240}
=11/120
$