9x-6/2x=3

Solution for 9x-6/2x=3 equation:

9x-6/2x=3

We move all terms to the left:

9x-6/2x-(3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


9x*2x-3*2x-6=0

Wy multiply elements

18x^2-6x-6=0

a = 18; b = -6; c = -6;
Δ = b2-4ac
Δ = -62-4·18·(-6)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{13}}{2*18}=\frac{6-6\sqrt{13}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{13}}{2*18}=\frac{6+6\sqrt{13}}{36}
$