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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-5)!=0

x∈R


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

Wy multiply elements

36x^2+240x^2+36x+(-32x)=0

We get rid of parentheses

36x^2+240x^2+36x-32x=0

We add all the numbers together, and all the variables

276x^2+4x=0

a = 276; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·276·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*276}=\frac{-8}{552}
=-1/69
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*276}=\frac{0}{552}
=0
$