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

Solution for 3x-2/(2x-7)=0 equation:

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


Domain of the equation: (2x-7)!=0

We move all terms containing x to the left, all other terms to the right

2x!=7

x!=7/2

x!=3+1/2

x∈R


We multiply all the terms by the denominator


3x*(2x-7)-2=0

We multiply parentheses

6x^2-21x-2=0

a = 6; b = -21; c = -2;
Δ = b2-4ac
Δ = -212-4·6·(-2)
Δ = 489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{489}}{2*6}=\frac{21-\sqrt{489}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{489}}{2*6}=\frac{21+\sqrt{489}}{12}
$