6/3x+4=26/2x

Solution for 6/3x+4=26/2x equation:

6/3x+4=26/2x

We move all terms to the left:

6/3x+4-(26/2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6/3x-(+26/2x)+4=0

We get rid of parentheses

6/3x-26/2x+4=0

We calculate fractions


12x/6x^2+(-78x)/6x^2+4=0

We multiply all the terms by the denominator


12x+(-78x)+4*6x^2=0

Wy multiply elements

24x^2+12x+(-78x)=0

We get rid of parentheses

24x^2+12x-78x=0

We add all the numbers together, and all the variables

24x^2-66x=0

a = 24; b = -66; c = 0;
Δ = b2-4ac
Δ = -662-4·24·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-66}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+66}{2*24}=\frac{132}{48}
=2+3/4
$