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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


9x/12x^2+(-4x)/12x^2-3-2=0

We add all the numbers together, and all the variables

9x/12x^2+(-4x)/12x^2-5=0

We multiply all the terms by the denominator


9x+(-4x)-5*12x^2=0

Wy multiply elements

-60x^2+9x+(-4x)=0

We get rid of parentheses

-60x^2+9x-4x=0

We add all the numbers together, and all the variables

-60x^2+5x=0

a = -60; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-60)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-60}=\frac{-10}{-120}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-60}=\frac{0}{-120}
=0
$