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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


48x^2/48x^2+16x/48x^2+36x/48x^2-3=0

Fractions to decimals

16x/48x^2+36x/48x^2-3+1=0

We multiply all the terms by the denominator


16x+36x-3*48x^2+1*48x^2=0

We add all the numbers together, and all the variables

52x-3*48x^2+1*48x^2=0

Wy multiply elements

-144x^2+48x^2+52x=0

We add all the numbers together, and all the variables

-96x^2+52x=0

a = -96; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-96)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-96}=\frac{-104}{-192}
=13/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-96}=\frac{0}{-192}
=0
$