4/3x-7/3=-3/2x-6

Solution for 4/3x-7/3=-3/2x-6 equation:

4/3x-7/3=-3/2x-6

We move all terms to the left:

4/3x-7/3-(-3/2x-6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

4/3x+3/2x+6-7/3=0

We calculate fractions


8x/54x^2+81x/54x^2+(-14x)/54x^2+6=0

We multiply all the terms by the denominator


8x+81x+(-14x)+6*54x^2=0

We add all the numbers together, and all the variables

89x+(-14x)+6*54x^2=0

Wy multiply elements

324x^2+89x+(-14x)=0

We get rid of parentheses

324x^2+89x-14x=0

We add all the numbers together, and all the variables

324x^2+75x=0

a = 324; b = 75; c = 0;
Δ = b2-4ac
Δ = 752-4·324·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-75}{2*324}=\frac{-150}{648}
=-25/108
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+75}{2*324}=\frac{0}{648}
=0
$