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

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

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

We move all terms to the left:

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

We calculate fractions


81x/108x^2+(-4x)/108x^2+(-8x)/108x^2+5=0

We multiply all the terms by the denominator


81x+(-4x)+(-8x)+5*108x^2=0

Wy multiply elements

540x^2+81x+(-4x)+(-8x)=0

We get rid of parentheses

540x^2+81x-4x-8x=0

We add all the numbers together, and all the variables

540x^2+69x=0

a = 540; b = 69; c = 0;
Δ = b2-4ac
Δ = 692-4·540·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-69}{2*540}=\frac{-138}{1080}
=-23/180
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+69}{2*540}=\frac{0}{1080}
=0
$