-7/3x-1/3=1/4x-3

Solution for -7/3x-1/3=1/4x-3 equation:

-7/3x-1/3=1/4x-3

We move all terms to the left:

-7/3x-1/3-(1/4x-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

-7/3x-1/4x+3-1/3=0

We calculate fractions


(-28x)/108x^2+(-27x)/108x^2+(-4x)/108x^2+3=0

We multiply all the terms by the denominator


(-28x)+(-27x)+(-4x)+3*108x^2=0

Wy multiply elements

324x^2+(-28x)+(-27x)+(-4x)=0

We get rid of parentheses

324x^2-28x-27x-4x=0

We add all the numbers together, and all the variables

324x^2-59x=0

a = 324; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·324·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*324}=\frac{0}{648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*324}=\frac{118}{648}
=59/324
$