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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


48x^2/48x^2+32x/48x^2+(-36x)/48x^2+5=0

Fractions to decimals

32x/48x^2+(-36x)/48x^2+5+1=0

We multiply all the terms by the denominator


32x+(-36x)+5*48x^2+1*48x^2=0

Wy multiply elements

240x^2+48x^2+32x+(-36x)=0

We get rid of parentheses

240x^2+48x^2+32x-36x=0

We add all the numbers together, and all the variables

288x^2-4x=0

a = 288; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·288·0
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*288}=\frac{0}{576}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*288}=\frac{8}{576}
=1/72
$