3x-5/2x=6

Solution for 3x-5/2x=6 equation:

3x-5/2x=6

We move all terms to the left:

3x-5/2x-(6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-6*2x-5=0

Wy multiply elements

6x^2-12x-5=0

a = 6; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·6·(-5)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{66}}{2*6}=\frac{12-2\sqrt{66}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*6}=\frac{12+2\sqrt{66}}{12}
$