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

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

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

We move all terms to the left:

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

We calculate fractions


(-4x)/108x^2+(-135x)/108x^2+(-8x)/108x^2+3=0

We multiply all the terms by the denominator


(-4x)+(-135x)+(-8x)+3*108x^2=0

Wy multiply elements

324x^2+(-4x)+(-135x)+(-8x)=0

We get rid of parentheses

324x^2-4x-135x-8x=0

We add all the numbers together, and all the variables

324x^2-147x=0

a = 324; b = -147; c = 0;
Δ = b2-4ac
Δ = -1472-4·324·0
Δ = 21609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21609}=147$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-147)-147}{2*324}=\frac{0}{648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-147)+147}{2*324}=\frac{294}{648}
=49/108
$