6/4x+2/3x=1

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

6/4x+2/3x=1

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


18x/12x^2+8x/12x^2-1=0

We multiply all the terms by the denominator


18x+8x-1*12x^2=0

We add all the numbers together, and all the variables

26x-1*12x^2=0

Wy multiply elements

-12x^2+26x=0

a = -12; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-12)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*-12}=\frac{-52}{-24}
=2+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-12}=\frac{0}{-24}
=0
$