3/4x+1/2=-5-2/3x

Solution for 3/4x+1/2=-5-2/3x equation:

3/4x+1/2=-5-2/3x

We move all terms to the left:

3/4x+1/2-(-5-2/3x)=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-(-2/3x-5)+1/2=0

We get rid of parentheses

3/4x+2/3x+5+1/2=0

We calculate fractions


36x^2/48x^2+36x/48x^2+32x/48x^2+5=0

We multiply all the terms by the denominator


36x^2+36x+32x+5*48x^2=0

We add all the numbers together, and all the variables

36x^2+68x+5*48x^2=0

Wy multiply elements

36x^2+240x^2+68x=0

We add all the numbers together, and all the variables

276x^2+68x=0

a = 276; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·276·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*276}=\frac{-136}{552}
=-17/69
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*276}=\frac{0}{552}
=0
$