3/4x+2=71/3x

Solution for 3/4x+2=71/3x equation:

3/4x+2=71/3x

We move all terms to the left:

3/4x+2-(71/3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(+71/3x)+2=0

We get rid of parentheses

3/4x-71/3x+2=0

We calculate fractions


9x/12x^2+(-284x)/12x^2+2=0

We multiply all the terms by the denominator


9x+(-284x)+2*12x^2=0

Wy multiply elements

24x^2+9x+(-284x)=0

We get rid of parentheses

24x^2+9x-284x=0

We add all the numbers together, and all the variables

24x^2-275x=0

a = 24; b = -275; c = 0;
Δ = b2-4ac
Δ = -2752-4·24·0
Δ = 75625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{75625}=275$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-275)-275}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-275)+275}{2*24}=\frac{550}{48}
=11+11/24
$