2x-6/3x+7=0

Solution for 2x-6/3x+7=0 equation:

2x-6/3x+7=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x+7*3x-6=0

Wy multiply elements

6x^2+21x-6=0

a = 6; b = 21; c = -6;
Δ = b2-4ac
Δ = 212-4·6·(-6)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{65}}{2*6}=\frac{-21-3\sqrt{65}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{65}}{2*6}=\frac{-21+3\sqrt{65}}{12}
$