4/3x-7=2x-3

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

4/3x-7=2x-3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-2x*3x+3*3x-7*3x+4=0

Wy multiply elements

-6x^2+9x-21x+4=0

We add all the numbers together, and all the variables

-6x^2-12x+4=0

a = -6; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·(-6)·4
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*-6}=\frac{12-4\sqrt{15}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*-6}=\frac{12+4\sqrt{15}}{-12}
$